A particle is travelling in a clockwise direc | vedclass

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

Question

(B) The equation of the ellipse is $\frac{x^2}{100} + \frac{y^2}{25} = 1$. The equation of the tangent at point $(x_1, y_1) = (-8, 3)$ is given by $\f

Vedclass · Accepted Answer

$\left(0, \frac{25}{3}\right)$

Vedclass · Answer

(B) The equation of the ellipse is $\frac{x^2}{100} + \frac{y^2}{25} = 1$. The equation of the tangent at point $(x_1, y_1) = (-8, 3)$ is given by $\frac{x x_1}{a^2} + \frac{y y_1}{b^2} = 1$. Substituting the values: $\frac{x(-8)}{100} + \frac{y(3)}{25} = 1$. Simplifying the equation: $-\frac{2x}{25} + \frac{3y}{25} = 1$,which gives $-2x + 3y = 25$. To find the point where the particle crosses the $Y$-axis,we set $x = 0$. Substituting $x = 0$ into the tangent equation: $3y = 25$,which gives $y = \frac{25}{3}$. Thus,the point is $\left(0, \frac{25}{3}\right)$.

$A$ particle is travelling in a clockwise direction on the ellipse $\frac{x^2}{100} + \frac{y^2}{25} = 1$. If the particle leaves the ellipse at the point $(-8, 3)$ and travels along the tangent to the ellipse at that point,then the point where the particle crosses the $Y$-axis is:

Similar Questions

If $S$ and $S^{\prime}$ are the foci of an ellipse $\frac{x^2}{169}+\frac{y^2}{144}=1$ and the point $B$ lying on the positive $Y$-axis is one end of its minor axis,then the incenter of the triangle $SBS^{\prime}$ is

$AB$ is a variable chord of the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$. If $AB$ subtends a right angle at the origin $O$, then $\frac{1}{OA^2} + \frac{1}{OB^2}$ equals to

If the distance between the directrices is thrice the distance between the foci,then the eccentricity of the ellipse is

The line passing through the extremity $A$ of the major axis and extremity $B$ of the minor axis of the ellipse $x^2+9y^2=9$ meets its auxiliary circle at the point $M$. Then the area of the triangle with vertices at $A$,$M$,and the origin $O$ is

If a tangent having slope $m = \frac{1}{3}$ to the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1$ $(a > b)$ is a normal to the circle $(x + 1)^2 + (y + 1)^2 = 1$,then $a^2$ lies in the interval:

Vedclass Test Series

Exam Paper Generator

Online Exam Module