The Equation of chord of contact of x2-25 -y2-16-1 is 4x -5y -20 -0 Find the point from which the tangents are drawn

Let the point be (x_1,y_1). The equation of chord of contact is given by T = 0 ⇒xx_1/25+yy_1/16=1 .....(1) This is given as 4x + 5y 20 = 0 Or x/5+y4=1 ...

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Standard XIII

Mathematics

Chord of Contact: Ellipse

The Equation ...

Question

The Equation of chord of contact of $\frac{x^{2}}{25} + \frac{y^{2}}{16} = 1 i s 4 x + 5 y - 20 = 0$ Find the point from which the tangents are drawn

(4, 5)

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(6, 5)

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(4, 6)

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(5, 4)

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Solution

The correct option is D
(5, 4)

Let the point be (x_1,y_1).
The equation of chord of contact is given by T = 0

$\Rightarrow \frac{x x_{1}}{25} + \frac{y y_{1}}{16} = 1$ .....(1)

This is given as 4x + 5y - 20 = 0

$O r \frac{x}{5} + y 4 = 1$ ....(2)

$\Rightarrow$ Comparing (1) and (2)

$\Rightarrow \frac{x_{1}}{25} = \frac{1}{5} a n d \frac{y_{1}}{16} = \frac{1}{4}$

$\Rightarrow (x_{1}, y_{1}) = (5, 4)$

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The Equation of chord of contact of x225+y216=1is4x+5y−20=0 Find the point from which the tangents are drawn

The correct option is D (5, 4) Let the point be (x_1,y_1). The equation of chord of contact is given by T = 0 ⇒xx125+yy116=1 .....(1) This is given as 4x + 5y - 20 = 0 Orx5+y4=1 ....(2) ⇒ Comparing (1) and (2) ⇒x125=15andy116=14 ⇒(x1,y1)=(5,4)

The Equation of chord of contact of $\frac{x^{2}}{25} + \frac{y^{2}}{16} = 1 i s 4 x + 5 y - 20 = 0$ Find the point from which the tangents are drawn