If the tangent to the curve frac{x^2}{a^2} + | vedclass

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

Question

(C) Differentiating the given equation $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ with respect to $x$,we get:$\frac{2x}{a^2} + \frac{2y}{b^2} \frac{dy}{d

Vedclass · Accepted Answer

$(0, \pm b)$

Vedclass · Answer

(C) Differentiating the given equation $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ with respect to $x$,we get:$\frac{2x}{a^2} + \frac{2y}{b^2} \frac{dy}{dx} = 0$Solving for $\frac{dy}{dx}$,we get:$\frac{dy}{dx} = -\frac{b^2 x}{a^2 y}$If the tangent is parallel to the $x$-axis,its slope must be zero:$\frac{dy}{dx} = 0 \implies -\frac{b^2 x}{a^2 y} = 0 \implies x = 0$Substituting $x = 0$ into the original equation of the ellipse:$\frac{0^2}{a^2} + \frac{y^2}{b^2} = 1 \implies y^2 = b^2 \implies y = \pm b$Therefore,the points of tangency are $(0, \pm b)$.

If the tangent to the curve $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ is parallel to the $x$-axis,then what is the point of tangency?

Similar Questions

The length of the latus rectum of $x^2+3y^2=12$ is

If the distance between the foci of an ellipse is $6$ and the length of the minor axis is $8$,then the eccentricity is

The distance between the directrices of the ellipse $\frac{x^2}{36}+\frac{y^2}{20}=1$ is

Consider a tangent to the ellipse $\frac{x^{2}}{2}+\frac{y^{2}}{1}=1$ at any point. The locus of the midpoint of the portion intercepted between the axes is

Given the base of a triangle and the sum of its other two sides,the locus of the center of its incircle is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module