Let the director circle of the hyperbola be denoted by and let director circle of ellipse be denoted by and is also the director circle of and let and be the eccentricities of the ellipse and hyperbola respectively. Then is equal to

Question

Let the director circle of the hyperbola $H : \frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1 (a > b)$ be denoted by $C_{1}$ and let director circle of ellipse $E : \frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = \frac{1}{3} (a > b)$ be denoted by $C_{2}$ and $C_{2}$ is also the director circle of $C_{1}$ and let $e_{1}$ and $e_{2}$ be the eccentricities of the ellipse $E$ and hyperbola $H$ respectively. Then $\frac{e_{2}^{2}}{e_{1}^{2}}$ is equal to

Smart Achievers · Accepted Answer

(3)

Ortho-centres of triangles formed by three tangents and corresponding normal to a parabola are equidistant from axis of parabola.

Solution

1 18

2 12

3 6

4 24

Ans.
(3)

Ortho-centres of triangles formed by three tangents and corresponding normal to a parabola are equidistant from axis of parabola.

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