The equation of the normal to the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$ at the point $(a\cos \theta ,\;b\sin \theta )$ is
The equation of the normal to the ellipse $\frac{{{x^2}}}{{{a^2}}} + \frac{{{y^2}}}{{{b^2}}} = 1$ at the point $(a\cos \theta ,\;b\sin \theta )$ is
- A
$\frac{{ax}}{{\sin \theta }} - \frac{{by}}{{\cos \theta }} = {a^2} - {b^2}$
- B
$\frac{{ax}}{{\sin \theta }} - \frac{{by}}{{\cos \theta }} = {a^2} + {b^2}$
- C
$\frac{{ax}}{{\cos \theta }} - \frac{{by}}{{\sin \theta }} = {a^2} - {b^2}$
- D
$\frac{{ax}}{{\cos \theta }} - \frac{{by}}{{\sin \theta }} = {a^2} + {b^2}$
Similar Questions
Let $E$ be the ellipse $\frac{{{x^2}}}{9} + \frac{{{y^2}}}{4} = 1$ and $C$ be the circle ${x^2} + {y^2} = 9$. Let $P$ and $Q$ be the points $(1, 2)$ and $(2, 1)$ respectively. Then
Let $E$ be the ellipse $\frac{{{x^2}}}{9} + \frac{{{y^2}}}{4} = 1$ and $C$ be the circle ${x^2} + {y^2} = 9$. Let $P$ and $Q$ be the points $(1, 2)$ and $(2, 1)$ respectively. Then
- [IIT 1994]
A man running round a race-course notes that the sum of the distance of two flag-posts from him is always $10$ metres and the distance between the flag-posts is $8$ metres. The area of the path he encloses in square metres is
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In an ellipse, with centre at the origin, if the difference of the lengths of major axis and minor axis is $10$ and one of the foci is at $(0, 5\sqrt 3 )$, then the length of its latus rectum is
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- [JEE MAIN 2019]
Let $P\left(x_1, y_1\right)$ and $Q\left(x_2, y_2\right), y_1<0, y_2<0$, be the end points of the latus rectum of the ellipse $x^2+4 y^2=4$. The equations of parabolas with latus rectum $P Q$ are
$(A)$ $x^2+2 \sqrt{3} y=3+\sqrt{3}$
$(B)$ $x^2-2 \sqrt{3} y=3+\sqrt{3}$
$(C)$ $x^2+2 \sqrt{3} y=3-\sqrt{3}$
$(D)$ $x^2-2 \sqrt{3} y=3-\sqrt{3}$
Let $P\left(x_1, y_1\right)$ and $Q\left(x_2, y_2\right), y_1<0, y_2<0$, be the end points of the latus rectum of the ellipse $x^2+4 y^2=4$. The equations of parabolas with latus rectum $P Q$ are
$(A)$ $x^2+2 \sqrt{3} y=3+\sqrt{3}$
$(B)$ $x^2-2 \sqrt{3} y=3+\sqrt{3}$
$(C)$ $x^2+2 \sqrt{3} y=3-\sqrt{3}$
$(D)$ $x^2-2 \sqrt{3} y=3-\sqrt{3}$
- [IIT 2008]