The equation of the normal at the point (2, 3 | vedclass

Name: PDF Generator App | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(b) $\frac{{x - {x_1}}}{{{x_1}/{a^2}}} = \frac{{y - {y_1}}}{{{y_1}/{b^2}}}$,

which is the standard equation of normal at point $({x_1},\,{y_1})$.

Vedclass · Accepted Answer

$3y - 8x + 7 = 0$

Vedclass · Answer

(b) $\frac{{x - {x_1}}}{{{x_1}/{a^2}}} = \frac{{y - {y_1}}}{{{y_1}/{b^2}}}$,

which is the standard equation of normal at point $({x_1},\,{y_1})$.

In the given ellipse, ${a^2} = 20,\,{b^2} = \frac{{180}}{{16}}$.

Hence the equation of normal at the point $(2,\,3)$ is

$\frac{{x - 2}}{{2/20}} = \frac{{y - 3}}{{48/180}}$ ==> $40\,(x - 2) = 15(y - 3)$

==> $8x - 3y = 7$

==> $3y - 8x + 7 = 0$.

The equation of the normal at the point $(2, 3)$ on the ellipse $9{x^2} + 16{y^2} = 180$, is

Similar Questions

If the curves, $\frac{x^{2}}{a}+\frac{y^{2}}{b}=1$ and $\frac{x^{2}}{c}+\frac{y^{2}}{d}=1$ intersect each other at an angle of $90^{\circ},$ then which of the following relations is TRUE ?

Find the equation of the ellipse, with major axis along the $x-$ axis and passing through the points $(4,\,3)$ and $(-1,\,4)$

A man running a racecourse notes that the sum of the distances from the two flag posts from him is always $10 \,m$ and the distance between the flag posts is $8\, m$ Find the equation of the posts traced by the man.

Let $L$ be a common tangent line to the curves $4 x^{2}+9 y^{2}=36$ and $(2 x)^{2}+(2 y)^{2}=31$. Then the square of the slope of the line $L$ is ..... .

The length of the latus rectum of the ellipse $5{x^2} + 9{y^2} = 45$ is