Straight Lines Questions - JEE

The base of an isosceles triangle is the intercept made by the line x + 2y = 4 with the coordinate axes. If the equations of the equal sides be x = 4 and y = mx + c, then find the value of 8m + c.

If the coordinates of the middle points of the sides of a triangle are (1, 1), (2, -3) and (3, 4), find the vertices and the centroid of the triangle.

The possible number of triangle is:

A square, of each side 2, lies above the x-axis and has one vertex at the origin. If one of the sides passing through the origin makes an angle 30° with the positive direction of the x-axis, then the sum of the x-coordinates of the vertices of the square is

A ray of light coming from the point (2, 2√3) is incident at an angle 30° on the line x = 1 at the point A. The ray gets reflected on the line x = 1 and meets X-axis at the point B. Then, the line AB passes through the point

If C is the reflection of A(2, 4) in X-axis and B is the reflection of C in Y-axis, then |AB| is equal to

Let ($\alpha$, $\beta$) be the centroid of the triangle formed by the lines 15x - y = 82, 6x - 5y = -4 and 9x + 4y = 17. Then $\alpha$ + 2$\beta$ and 2$\alpha$ - $\beta$ are the roots of the equation

Let A (-3, 2) and B (-2, 1) be the vertices of a triangle ABC. If the centroid of triangle ABC lies on the line 3x + 4y + 2 = 0, then the locus of vertex C is :

(A) (5,4)

Let y = m1x and y = m2x be two straight lines represented by x2 − 2cxy − 7y2 = 0. If (m1 + m2) = 4m1m2, then the value of c is:

Let ${ }^{n} {C}_{r-1}=28,{ }^{n} {C}_{r}=56$ and ${ }^{n} {C}_{r+1}=70$. Let $A(4 cos\ t, 4 sin \ t), {B}(2 sin \ t,-2$ cos t) and ${C}\left(3 r-n, r^{2}-n-1\right)$ be the vertices of a triangle ABC, where t is a parameter. If $(3 x-1)^{2}+(3 y)^{2}=\alpha$, is the locus of the centroid of triangle ABC, then $\alpha$ equals

If p and p′ be perpendiculars from the origin upon the straight lines $x \sec \theta + y \csc \theta = a$ and $x \cos \theta - y \sin \theta = a \cos 2\theta$ respectively, then the value of the expression $4p^2 + p'^2$ is

Let $ABCD$ be a parallelogram whose equations for the diagonals $AC$ and $BD$ are $x + 2y = 3$ and $2x + y = 3$, respectively. If length of diagonal $AC = 4$ units and area of parallelogram $ABCD = 8$ sq. units, then the length of other diagonal $BD$ is

Transform the equation $14x^2 - 4xy + 11y^2 - 36x + 48y + 41 = 0$ to the form $ax'^2 + by'^2 = 1$ by suitable change of axes.

A triangle has a vertex at (1, 2) and the mid points of the two sides through it are (−1, 1) and (2, 3). Then the centroid of this triangle is

If $D$, $E$ and $F$ are the middle points of $BC$, $CA$ and $AB$ respectively then the area of the triangle $DEF$ is:

Lines are drawn parallel to the line $4x - 3y + 2 = 0$, at a distance $\dfrac{3}{5}$ from the origin. Then which one of the following points lies on any of these lines?

The complete set of real values of 'a' such that the point $P(a, \sin a)$ lies inside the triangle formed by the lines $x - 2y + 2 = 0$, $x + y = 0$ and $x - y - p = 0$, is:

A pair of lines is given by $ax^2 + 2hxy + by^2 = 0$. If point $(x_1, y_1)$ lies on one of the lines, find the relationship between the coefficients $a$, $b$, and $h$.

Let B(1, –3) and D(0, 4) represent two vertices of rhombus ABCD in the (x, y) plane, then coordinates of vertex A if ∠BAD = 60° can be equal to:

If a straight line passing through the point P(- 3, 4) is such that its intercepted portion between the coordinate axes is bisected at P, then its equation is

The area of triangle PAB where P lies on the line x + y = 3, and A and B are the intercepts of another line with the axes, is given. Find the area of triangle PAB if |PA| = |PB| = 2.

Let $ABC$ be a triangle. Let $A$ be the point $(1, 2)$, $y = x$ is the perpendicular bisector of $AB$ and $x - 2y + 1 = 0$ is the angle bisector of angle $C$. If the equation of $BC$ is given by $ax + by - 5 = 0$ then the value of $a + b$ is ______.

The incentre of the triangle with vertices $(1,\sqrt{3})$, $(0,0)$ and $(2,0)$ is

A ray of light passing through the point $A(1, 2)$ is reflected at a point $B$ on the x-axis and then passes through $(5, 3)$. Then the equation of AB is:

Two equal sides $AB$ and $AC$ of an acute angle triangle $ABC$ are formed by the equations $7x - y + 3 = 0$ and $x + y - 3 = 0$, side $BC$ is $ax + by - 31 = 0$ where $a - 10b = 31$. Value of $2a + 10b + 31 = 0$ is ____.

In triangle $ABC$ if the median to side $BC$ has length $\left[11 - 6\sqrt{3}\right]^{\frac{1}{2}}$ and it divides angle $\angle A$ into angles $30°$ and $45°$. Then length of side $BC$ is __________.

In triangle ABC, the angle between lines AC and AB can be found using the formula for the angle between two lines. If the slope of AC is $\frac{1}{4}$ and tan θ₁ = $\frac{1}{3}$, find the slope m of AB such that tan θ₂ = $\frac{1}{m}$.

Consider a trapezoid ABCD, one of whose non parallel sides AB which is 8 cm long is perpendicular to the base. The base BC and AD of trapezoid are 6 cm and 10 cm in lengths respectively. Let $L_1, L_2, L_3, L_4$ represent the lines AB, BC, CD and DA respectively and $d(P, L)$ denote the perpendicular distance of point P from line L.Find the area of region inside the trapezoid ABCD in which the point Q can lie satisfying $d(Q, L_4) \leq d(Q, L_3)$:

The slopes of three sides of a triangle $ABC$ are $-1, -2, 3$ respectively. If the orthocenter of triangle $ABC$ is origin, then the locus of its centroid is $y = \frac{a}{b}x$ where $a, b$ are relatively prime than $b - a$ is equal to ________.

Three lines $2x + 11y - 5 = 0$, $24x + 7y - 20 = 0$ and $4x - 3y - 2 = 0$ are given. Which of the following is correct?

Find the coordinates of point F given that \frac{BF}{CF} = \frac{BE}{AC} = \frac{a}{4} where B(0,a), C(a,a), and A(a,0).

If the slope of one of the line represented by $ax^2 + 2hxy + by^2 = 0$ is the square of the other, then the value of $\frac{a + b}{h} - \frac{8h^2}{ab}$ is ____.

Find the value of $c$ such that $2 \times \left(1 - \frac{c}{9}\right)(9 - c) = \frac{1}{2} \times 8 \times 1$.

The slopes of three sides of a triangle $ABC$ are $-1, -2, 3$ respectively. If the orthocenter of triangle $ABC$ is origin, then the locus of its centroid is $y = \frac{a}{b}x$ where $a, b$ are relatively prime then $b - a$ is equal to ____.

Let $\triangle ABC$ be an isosceles triangle with $AB = AC$. If $AB : 4x + y = 7$, $AC : x + 4y = 7$ and $BC$ is passing through $(1, 1)$, then possible equation of $BC$ is:

A line passes through the origin and point $(8, 11)$. Find the equation of this line.

The sides of a triangle are the straight lines $x + y = 1$, $7y = x$ and $3y + x = 0$. Then which of the following is an interior point of the triangle:

If one vertex of an equilateral triangle of side 'a' lies at origin and the other lies on the line $x - \sqrt{3}y = 0$, then the coordinates of the third vertex are:

A straight line through the point $A(-2, -3)$ cuts the lines $x + 3y = 9$ and $x + y + 1 = 0$ at $B$ and $C$ respectively. If $AB.AC = 20$, then product of slopes of line is____.

A possible equation of L is:

If the points where the lines $3x - 2y - 12 = 0$ and $x + ky + 3 = 0$ intersect both the coordinate axes are concyclic, then the number of possible real values of $k$ is:

In an acute triangle ABC, point H is the intersection point of altitude CE to AB and altitude BD to AC. A circle with DE as its diameter intersects AB and AC at points F and G respectively. If BC = 25, BD = 20 and BE = 7.The sum of the length of all the sides of △ABC is:

The circle 'S' touches the sides AB and AD of the rectangle ABCD and cuts the side DC at a single point F and the side BC at a single point E. If |AB| = 32, |AD| = 40 and |BE| = 1.The area of trapezoid AFCB is:

Let A(1, 1) and B(3, 3) be two fixed points and P be a variable point such that the area of ∆PAB remains constant equal to 1 for all positions of P. Then the locus of P is given by:

Perpendicular distance of the line AB from the point (2, 2) is:

A point on the straight line, $3x + 5y = 15$ which is equidistant from the coordinate axes will lie only in

Two vertices of a triangle are $(0, 2)$ and $(4, 3)$ and its orthocenter is at the origin. Then the third vertex $A(a, b)$ lies in which quadrant?

Find the y-intercept of the line passing through points with slope 2, where the point lies at distance 5 from (0, 2).

Let A = (0, 0), B = (4, 0) and on segment AB is given a point M. On the same side of AB, squares AMCD and BMFE are constructed above AB. The circumcircles S₁ and S₂ of two squares AMCD and BMFE respectively have centres P and Q.The locus of midpoints of all segments PQ as M varies along the segment AB is:

Straight Lines Questions (433)