Tag: conic section
Questions Related to conic section
Let the equation of a circle and a parabola be $x^2+y^2-4x-6=0$ and $y^2=9x$ respectively. Then
The condition that the straight line $\displaystyle lx + my + n = 0$ touches the parabola $\displaystyle x^2 = 4ay$ is
The length of the chord of the parabola $y^2 = x$ which is bisected at the point $(2, 1)$ is
If $2$ and $3$ are the length of the segments of any focal chord of a parabola $y^2 = 4ax$, then value of $2a$ is
If the line $y- \sqrt x +3 = 0$ cuts the parabola $y^2 = x + 2$ at $A$ and $B$, and if $P$ $(3,\ 0)$, then $PA.PB$ is equal to
The
eccentricity of the hyperbola whose asymptotes are $3x + 4y = 2{\text{ and }}4x - 3y + 5 = 0$
The equation of the conjugate axis of the hyperbola $\frac{{{{\left( {y - 2} \right)}^2}}}{9} - \frac{{{{\left( {x + 3} \right)}^2}}}{{16}} = 1$ is
The eccentricity of the conjugate hyperbola of the hyperbola $x^{2} - 3y^{2} = 1$ is
If variable has its interceptson the coordinates axes $e$ and $e'$ where $e/2$ and $e'/2$ are the eccentricities of hyperbola and conjugate hyperbola, Then the line always touches the circle $x^{2}+y^{2}=r^{2}$, where $r=$
Let $e$ be the eccentricity of a hyperbola $\dfrac{x^{2}}{a^{2}}-\dfrac{y^{2}}{b^{2}}=1$, and $f(e)$ be the eccentricity of hyperbola $-\dfrac{x^{2}}{a^{2}}+\dfrac{y^{2}}{b^{2}}=1$, then $\displaystyle \int _{ 1 }^{ 3 } \underbrace { fff.....f\left( e \right) } _{ n\quad times } de$ is equal to
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