Tag: maths

The value of $\cfrac { { 2 }^{ 2n-2 } }{ { 2 }^{ n(n-1) } }-\cfrac { { 8 }^{ n-1 } }{ { 2 }^{ (n-1)(n+1) } } $ will be

Find the sum of all values of $x$, so that $16^{\left(x^{2}+3x-1\right)}=8^{\left(x^{2}+3x+2\right)}$.

If  $n$  is a natural number, then  $4 ^ { n } - 3 ^ {  n }$  ends with a digit  $x.$  The number of possible values of  $x$  is

If a normal is drawn at point $P$ of ellipse $ \dfrac{x^{2}}{a^{2}}+\dfrac{y^{2}}{b^{2}}=1$, then the maximum distance from centre of ellipse will be $a-b$ 

If the normal at any point $P$ of the ellipse $\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} = 1$ meets the axes in $G$ and $g$ respectively, then $|PG| : |Pg|$ is equal to 

One foot of normal of the ellipse $4x^2$ $+$ 9$y^2$ $= 36 $, that is parallel to the line $2x + y = 3 $, is

If the normal at any point on the ellipse $\dfrac { { x }^{ 2 } }{ { a }^{ 2 } } +\dfrac { { y }^{ 2 } }{ { b }^{ 2 } } =1$ meets the axes in $G$ and $g$ respectively, then $PG:Pg=$

The equation of normal at the point $(0, 3)$ of the ellipse $9x^2 + 5y^2 = 45$ is

Find the equation of the normal to the ellipse $9x^2 + 16y^2 = 288$ at the point $(4, 3).$

The line $y=mx-\dfrac{\left(a^{2}-b^{2}\right)m}{\sqrt{a^{2}b^{2}m^{2}}}$ is normal to  the ellipse $\dfrac{x^{2}}{a^{2}}+\dfrac{y^{2}}{b^{2}}=1$ for all values of $m$ belongs to