Parabola
General
Grade 11
Question:
A parabola y = ax<span class="math-inline">^2</span> + bx + c crosses the x-axis at (\(\alpha\),0) (\(\beta\),0) both to the right of the origin. A circle also passes through these two points. The length of a tangent from the origin to the circle is :
<span class="math-inline">\(\sqrt{\frac{bc}{a}}\)</span>
<span class="math-inline">\(ac^2\)</span>
<span class="math-inline">\(\frac{b}{a}\)</span>
<span class="math-inline">\(\sqrt{\frac{c}{a}}\)</span>
Step-by-Step Solution
Key Concept: General
Prove that the common tangent of the ellipse \( \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 \) and \( \frac{x^2}{b^2} + \frac{y^2}{a^2} = 0 \) subtends a right angle at the origin.
Correct Answer: 2