What is the equation of chord of the ellipse x2-a2-y2-b2-1 whose middle point is x1- y1 - You are given- T-xx1-a2-yy1-b2-1 and S1 x12-a2-y12-b2-1

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Byju's Answer

Standard XIII

Mathematics

Chord with a Given Mid Point : Ellipse

What is the e...

Question

What is the equation of chord of the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ whose middle point is $(x_{1}, y_{1})$ ? You are given. $T = \frac{x x_{1}}{a^{2}} + \frac{y y_{1}}{b^{2}} - 1 a n d S_{1} \frac{x_{1}^{2}}{a^{2}} + \frac{y_{1}^{2}}{b^{2}} - 1$

$T + S_{1} = 0$

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$T = S_{1}$

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$T + S_{1} = 1$

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$T + 1 = S_{1}$

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Solution

The correct option is B
$T = S_{1}$

$T = S_{1}$ gives the chord with a given middle point $(x_{1}, y_{1})$ . This result is true for any conic. The derivation of this is not important. We recommend you to remember this as it is same for all the conics.

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Similar questions

What is the equation of chord of the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ whose middle point is $(x_{1}, y_{1})$ ? You are given. $T = \frac{x x_{1}}{a^{2}} + \frac{y y_{1}}{b^{2}} - 1 a n d S_{1} \frac{x_{1}^{2}}{a^{2}} + \frac{y_{1}^{2}}{b^{2}} - 1$

Q. Assertion :Statement - 1 : The equation of the chord of contact of tangents drawn from the point

(2, - 1)

to the hyperbola

16 x^{2} - 9 y^{2} = 144

32 x + 9 y = 144

Reason: Statement-2: Pair of tangents drawn from

(x_{1}, y_{1})

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

S S_{1} = T^{2}

S = \frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} - 1, S_{1} = \frac{x_{1}^{2}}{a^{2}} - \frac{y_{1}^{2}}{b^{2}} - 1

T = \frac{x x_{1}}{a^{2}} - \frac{y y_{1}}{b^{2}} - 1

If for the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1, S_{1} = \frac{x_{1}^{2}}{a^{2}} + \frac{y_{1}^{2}}{b^{2}} - 1$ , for point $(x_{1}, y_{1})$ , Which of the following is true

Q. Equation of chord of the hyperbola

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

whose mid point is

(x_{1}, y_{1})

is given by

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What is the equation of chord of the ellipse x2a2+y2b2=1 whose middle point is (x1,y1) ? You are given. T=xx1a2+yy1b2−1andS1x21a2+y21b2−1

The correct option is B T=S1 T=S1 gives the chord with a given middle point (x1,y1). This result is true for any conic. The derivation of this is not important. We recommend you to remember this as it is same for all the conics.

What is the equation of chord of the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ whose middle point is $(x_{1}, y_{1})$ ? You are given. $T = \frac{x x_{1}}{a^{2}} + \frac{y y_{1}}{b^{2}} - 1 a n d S_{1} \frac{x_{1}^{2}}{a^{2}} + \frac{y_{1}^{2}}{b^{2}} - 1$

The correct option is B
$T = S_{1}$

$T = S_{1}$ gives the chord with a given middle point $(x_{1}, y_{1})$ . This result is true for any conic. The derivation of this is not important. We recommend you to remember this as it is same for all the conics.