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If angle betw...

Question

If angle between tangents from the point $(h, k)$ to ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ is right angle then $h^{2} + k^{2} = a^{2} + b^{2} .$

A

True

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B

False

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Solution

The correct option is A True

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Similar questions

Q. If the tangent line to an ellipse

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1

cuts intercepts

h

k

\frac{a^{2}}{h^{2}} + \frac{b^{2}}{k^{2}} =

Q. If any tangent to

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1

intercepts lengths

h

k

on the axes, then

\frac{a^{2}}{h^{2}} + \frac{b^{2}}{k^{2}} =

a, b

c

be positive real numbers. The following system of equations in

x, y

z

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} - \frac{z^{2}}{c^{2}} = 1, \frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} + \frac{z^{2}}{c^{2}} = 1, - \frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} + \frac{z^{2}}{c^{2}} = 1

E_{1} : \frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} - 1 = 0, (a > b)

E_{2} : \frac{x^{2}}{k^{2}} + \frac{y^{2}}{b^{2}} - 1 = 0, (k < b)

is inscribed in

E_{1} .

E_{1} and E_{2}

have same eccentricities and length of minor axis of

E_{2} = p \times Length of Latus rectum of E_{1}, then p =

Q. The angle between the curves

\frac{x^{2}}{a^{2} + k_{1}} + \frac{y^{2}}{b^{2} + k_{1}} = 1

\frac{x^{2}}{a^{2} + k_{2}} + \frac{y^{2}}{b^{2} + k_{2}} = 1

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