Tag: maths
Questions Related to maths
The number of normals that can be drawn to the curve $\displaystyle 4x^{2} + 9y^{2} = 36$ from an external point, in general, is
If the equation of normal to the ellipse $\displaystyle 4x^{2}+9y^{2}=36$ at the point $(3, -2)$ is $ px+qy=r$. Find the value of $p+q+r.$
Find the condition that the line $lx+my=n$ be a normal for ellipse
Find where the line $\displaystyle 2x+y=3$ cuts the curve $\displaystyle 4x^{2}+y^{2}=5.$ Obtain the equations of the normals at the points of intersection and determine the co-ordinates of the point where these normals cut each other.
If $y=mx+7\sqrt{3}$ is normal to $\dfrac{x^2}{18}-\dfrac{y^2}{24}=1$ then the value of m can be?
The normal at a point $P$ on the ellipse $x^{2}+4y^{2}=16$ meets the x-axis at $Q.$ If $M$ is the mid point of the line segment $PQ$, then locus of $M$ intersects the latus rectums of the given ellipse at the points.
The eccentric angle of the point where the line, $5x\, -\, 3y\, =\, 8\sqrt{2}$ is a normal to the ellipse $\displaystyle\frac{x^2}{25}\, +\, \frac{y^2}{9}\,=\,1$ is
On the ellipse $\displaystyle \frac { { x }^{ 2 } }{ 4 } +\frac { { y }^{ 2 } }{ 9 } =1$, one of the points at which the normals are parallel to the line $2x-y=1$ is
The equation of the normal to the ellipse $\displaystyle\frac{x^2}{a^2}\,+\,\frac{y^2}{b^2}\,=\,1$ at the positive end of latus rectum is :
Area of the triangle formed by the ${x}$ axis, the tangent and normal at $(3,2)$ to the ellipse $\displaystyle \frac{x^{2}}{18}+\frac{y^{2}}{8}=1$ is