Find the equation of tangent at -3-2-2-2 to the ellipse7x2- 7y2- 2xy - 10x - 10y - 7 - 0

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Point Form of Tangent: Ellipse

Find the equa...

Question

Find the equation of tangent at $(- \frac{3}{2}, \frac{2}{2})$ to the ellipse

$7 x^{2} + 7 y^{2} + 2 x y + 10 x - 10 y + 7 = 0$

$x + y = 0$

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$2 x + 22 y = 7$

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$2 x + 6 y = 6$

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$3 x + 5 y = 3$

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Solution

The correct option is B
$2 x + 22 y = 7$

The equation of tangent to any second degree curve $a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0 i s T = 0.$

T is obtained by replacing $x$ by $\frac{x + x_{1}}{2} y$ by $\frac{y + y_{1}}{2}, x^{2}$ by $x x_{1}, y^{2}$ by $y y,$ and $x y$ by $\frac{x y_{1} + y x_{1}}{2} .$

and keeping the constant as it is we will apply the same for the given equation and point.

$\Rightarrow$ Equation of tangent is

$\Rightarrow - 2 x - 22 y + 7 = 0$ or

$2 x + 22 y = 7$

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Similar questions

Find the equation of tangent at $(- \frac{3}{2}, \frac{2}{2})$ to the ellipse

$7 x^{2} + 7 y^{2} + 2 x y + 10 x - 10 y + 7 = 0$

Q. The equation of the ellipse with focus (-1,1), directrix x-y+3=0 and eccentricity 1/2 is

Q. The equation of an ellipse with focus at

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and eccentricity

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Q. The equation of the ellipse with focus (−1, 1), directrix x − y + 3 = 0 and eccentricity 1/2 is
(a) 7x² + 2xy + 7y² + 10x + 10y + 7 = 0
(b) 7x² + 2xy + 7y² + 10x − 10y + 7 = 0
(c) 7x² + 2xy + 7y² + 10x − 10y − 7 = 0
(d) none of these

Match the column

$\begin{matrix} Equation & Name of the curve 1) x^{2} - 2 x - y - 3 = 0 & P) Circle 2) x^{2} + 3 x y + 2 y^{2} - x - 4 y - 6 = 0 & Q) Parabola 3) x^{2} + y^{2} - 20 = 0 & R) Ellipse 4) 7 x^{2} + 7 y^{2} + 2 x y + 10 x - 10 y + 7 = 0 & S) Hyperbola 5) 6 x^{2} - x y - y^{2} - 23 x + 4 y + 15 = 0 & T) Pair of straight lines \end{matrix}$

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Find the equation of tangent at (−32,22) to the ellipse 7x2+ 7y2+ 2xy + 10x − 10y + 7 = 0

Find the equation of tangent at $(- \frac{3}{2}, \frac{2}{2})$ to the ellipse

$7 x^{2} + 7 y^{2} + 2 x y + 10 x - 10 y + 7 = 0$