Tag: maths
Questions Related to maths
The equation of the normal at the positive end of the latusrectum of the hyperbola $x^2-3y^2=144$ is
Which one of the following points does not lie on the normal to the hyperbola, $\cfrac { { x }^{ 2 } }{ 16 } -\cfrac { { y }^{ 2 } }{ 9 } =1$ drawn at the point $\left( 8,3\sqrt { 3 } \right) $?
Let $A\left( A\sec { \theta } ,3\tan { \theta } \right) $ and $B\left( A\sec { \phi } ,3\tan { \phi } \right) $ where $\theta +\phi =\cfrac { \pi }{ 2 } $, be two points on the hyperbola $\cfrac { { x }^{ 2 } }{ 4 } -\cfrac { { y }^{ 2 } }{ 9 } =1$. If $\left( \alpha ,\beta \right) $ is the point of intersection of normals to the hyperbola at $A$ and $B$, then $\beta=$
If the sum of the slopes of the normal from a point P to the hyperbola $xy = {c^2}$is equal to $\lambda (\lambda \in {R^ + })$,then the locus of point P is
Let $P\left( a\sec { \theta } ,b\tan { \theta } \right) $ and $Q\left( a\sec { \phi } ,b\tan { \phi } \right) $, where $\theta +\phi =\dfrac {\pi}{2} $, be the two points on the hyperbola $\cfrac { { x }^{ 2 } }{ { a }^{ 2 } } -\cfrac { { y }^{ 2 } }{ { b }^{ 2 } } =1$. If $(h,k)$ is the point of intersection of the normals of $P$ and $Q$, then $k$ is equal to
If a normal of slope $m$ to the parabola ${ y }^{ 2 }=4ax$ touches the hyperbola ${ x }^{ 2 }-{ y }^{ 2 }={ a^2 }$, then
If a normal of slope $m$ to the parabola $y^2 = 4ax$ touches the hyperbola $x^2 - y^2 = a^2$, then
Let P $(asec \theta,\, btan \theta)$ and Q $(asec \phi,\, btan \phi)$, where $\theta\, +\, \phi\, =\, \displaystyle \frac{\pi}{2}$, be two points on the hyperbola $\displaystyle \frac{x^2}{a^2}\, -\, \frac{y^2}{b^2}\, =\, 1$. If (h, k) is the point of intersection of the normals at P & Q, then k is equal to
From any point R two normals which are right angled to one another are drawn to the hyperbola $\displaystyle \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1,\left ( a>b \right )$ If the feet of the normals are P and Q then the locus of the circumcentre of the triangle PQR is
Sum of an even number and an odd number is always an odd number.