For the equation of ellipse- x2-4-y2-9-1- what does S1 correspond to

The correct option is C S_1 = xx_1/4 + yy_1/9 1We know for the equation x^2/a + y^2/b = 1, S_1 corresponds to S_1 = xx_1/a + yy_1/b 1. Therefore S1 corr ...

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Standard XII

Mathematics

Integration Using Substitution

For the equat...

Question

For the equation of ellipse, $\frac{x^{2}}{4} + \frac{y^{2}}{9} = 1,$ what does $S_{1}$ correspond to

S_{1} = \frac{x x_{1}}{4} + \frac{y y_{1}}{9} - 1

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S_{1} = \frac{x x_{1}}{2} + \frac{y y_{1}}{3} - 1

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S_{1} = \frac{x x_{1}}{4} + \frac{y y_{1}}{9} + 1

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S_{1} = \frac{x x_{1}}{4} + \frac{y y_{1}}{9}

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Solution

The correct option is A $S_{1} = \frac{x x_{1}}{4} + \frac{y y_{1}}{9} - 1$
We know for the equation $\frac{x^{2}}{a} + \frac{y^{2}}{b} = 1,$ $S_{1}$ corresponds to $S_{1} = \frac{x x_{1}}{a} + \frac{y y_{1}}{b} - 1$ . Therefore S1 corresponds to $S_{1} = \frac{x x_{1}}{4} + \frac{y y_{1}}{9} - 1$

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Similar questions

Q. For the equation of ellipse,

\frac{x^{2}}{4} + \frac{y^{2}}{9} = 1

what does S correspond to

Q. Equation of tangent at

(- 3, - 4)

to ellipse

\frac{x^{2}}{9} + \frac{y^{2}}{16} = 1

Q. An ellipse has eccentricity

\frac{1}{2}

and one of the foci at the point

S (\frac{1}{2}, 1) .

One of the directrices of the ellipse is the common tangent to the circle

x^{2} + y^{2} = 1

and the hyperbola

x^{2} - y^{2} = 1,

corresponding to the focus

S .

The equation of the ellipse in standard form is

Q. Consider equation of ellipses as:

E_{1} : \frac{x^{2}}{25} + \frac{y^{2}}{9} = 1

E_{2} : \frac{x^{2}}{9} + \frac{y^{2}}{4} = 1

E_{3} : \frac{x^{2}}{9} + \frac{y^{2}}{25} = 1

Which of the following is/are true?

Q. Equation of the common tangent to the ellipse

\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1

and the circle

x^{2} + y^{2} = 12

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For the equation of ellipse, x24+y29=1, what does S1 correspond to

The correct option is A S1=xx14+yy19−1We know for the equation x2a+y2b=1, S1 corresponds to S1=xx1a+yy1b−1. Therefore S1 corresponds to S1=xx14+yy19−1

For the equation of ellipse, $\frac{x^{2}}{4} + \frac{y^{2}}{9} = 1,$ what does $S_{1}$ correspond to

The correct option is A $S_{1} = \frac{x x_{1}}{4} + \frac{y y_{1}}{9} - 1$
We know for the equation $\frac{x^{2}}{a} + \frac{y^{2}}{b} = 1,$ $S_{1}$ corresponds to $S_{1} = \frac{x x_{1}}{a} + \frac{y y_{1}}{b} - 1$ . Therefore S1 corresponds to $S_{1} = \frac{x x_{1}}{4} + \frac{y y_{1}}{9} - 1$