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Byju's Answer

Standard XII

Mathematics

Auxiliary Circle of Hyperbola

If ' CF ' is ...

Question

If ‘CF’ is the perpendicular from the centre C of the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ on the tangent at any point P and G is the point where the normal at P meets the major axis, then CF.PG is

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Solution

The correct option is A
$C F = \frac{a b}{\sqrt{a^{2} s i n^{2} θ + b^{2} c o s^{2} θ}} P G = - \frac{b}{a} \sqrt{a^{2} s i n^{2} θ + b^{2} c o s^{2} θ}$

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If ‘CF’ is the perpendicular from the centre C of the ellipse x2a2+y2b2=1 on the tangent at any point P and G is the point where the normal at P meets the major axis, then CF.PG is

The correct option is A CF=ab√a2sin2θ+b2cos2θPG=−ba√a2sin2θ+b2cos2θ

If ‘CF’ is the perpendicular from the centre C of the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ on the tangent at any point P and G is the point where the normal at P meets the major axis, then CF.PG is

The correct option is A
$C F = \frac{a b}{\sqrt{a^{2} s i n^{2} θ + b^{2} c o s^{2} θ}} P G = - \frac{b}{a} \sqrt{a^{2} s i n^{2} θ + b^{2} c o s^{2} θ}$