Circles Question - None

Question

Statement-1: Tangents are drawn from the point $(17, 7)$ to the circle $x^2 + y^2 = 169$. The tangents are mutually perpendicular.
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Statement-2: The locus of the points from which mutually perpendicular tangents can be drawn to the given circle is $x^2 + y^2 = 338$.

Accepted Answer

Step 1: Identify the circle parameters

Given circle: x² + y² = 169

Here, r² = 169, so r = 13

Step 2: Verify Statement-2 (the locus condition)

For a circle x² + y² = r², the locus of points from which mutually perpendicular tangents can be drawn is the director circle: x² + y² = 2r²

For our circle: x² + y² = 2(169) = 338

Statement-2 is TRUE

Step 3: Verify Statement-1 by checking if (17,7) satisfies the director circle equation

Substitute (17, 7) into x² + y² = 338:

17² + 7² = 289 + 49 = 338 ✓

Since (17, 7) lies on the director circle x² + y² = 338, tangents drawn from (17, 7) to the circle x² + y² = 169 are indeed mutually perpendicular

Statement-1 is TRUE

Step 4: Determine the relationship

Statement-2 explains why Statement-1 is true. The tangents from (17, 7) are perpendicular precisely because (17, 7) lies on the director circle, which is the complete locus of all points with this property.

Statement-2 is a correct explanation for Statement-1

∴ Answer: (a) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1

Question:

Step-by-Step Solution

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