Sample QuestionsConic Sections questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
If the focus of the parabola is $(0, -3)$, its directrix is y $= 3$, then its equation is ________
- ✓
$x^2=-12 y$
- B
$x^2=12 y$
- C
$y^2=12 x$
- D
$y^2=-12 x$
Answer: A.
View full solution →The length of latus rectum of the parabola $x^2-4 x-8 y+12=0$ is
Answer: C.
View full solution →The line $y=m x+1$ is a tangent to the parabola $y^2=4 x$, if $m$ is
Answer: A.
View full solution →The foci of hyperbola $4 x^2-9 y^2-36=0$ are
Answer: A.
View full solution →If the line $2 x-y=4$ touches the hyperbola $4 x^2-3 y^2=24$, the point of contact is
Answer: C.
View full solution →Find the equations of the tangents to the hyperbola $3 x^2-y^2=48$ which are perpendicularto the line x + 2y – 7 = 0.
View full solution →Find the equation of the tangent to the ellipse $x^2+4 y^2=100$ at $(8,3)$.
View full solution →Find the equation of the tangent to the parabola $y^2=8 x$ at $t=1$ on it.
View full solution →Find the equation of the tangent to the parabola $y^2=9 x$ at the point $(4,-6)$ on it.
View full solution →Find the co-ordinates of a point of the parabola $y^2 = 8x$ having focal distance $10.$
View full solution →Find the equation of the tangent to the hyperbola, : $\frac{x^2}{25}-\frac{y^2}{16}=1$ at $P \left(30^{\circ}\right)$
View full solution →Find the equation of the tangent to the hyperbola, : $x=3 \sec \theta, y=5 \tan \theta$ at $\theta=\pi / 3$
View full solution →Find the equation of the tangent to the hyperbola, : $7 x^2-3 y^2=51$ at $(-3,-2)$
View full solution →Find the equation of the hyperbola in the standard form if : length of the conjugate axis is 3 and the distance between the foci is 5.
Find the equation of the hyperbola in the standard form if : eccentricity is $\frac{3}{2}$ and distance between foci is 12 .
View full solution →Two tangents to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ make angles $\theta_1, \theta_2$, with the transverse axis.Find the locus of their point of intersection if $\tan \theta_1+\tan \theta_2=k$.
View full solution →Show that the line $2 x-y=4$ touches the hyperbola $4 x^2-3 y^2=24$. Find the point of
View full solution →Tangents are drawn through a point $P$ to the ellipse $4 x^2+5 y^2=20$ having inclinations $\theta_1$and $\theta_2$ such that $\tan \theta_1+\tan \theta_2=2$. Find the equation of the locus of $P$.
View full solution →Show that the line $8 y+x=17$ touches the ellipse $x^2+4 y^2=17$. Find the point of contact.
View full solution →Find the equation of the tangent to the ellipse $\frac{x^2}{5}+\frac{y}{4}=1$ passing through the point (2,-2).
View full solution →Show that the product of the lengths of its perpendicular segments drawn from the foci toany tangent line to the ellipse $\frac{x^2}{25}+\frac{y^2}{16}=1$ is equal to 16 .
View full solution →Two tangents to the parabola $y ^2=8 x$ meet the tangents at the vertex in $P$ and $Q$. If $PQ =4$,prove that the locus of the point of intersection of the two tangents is $y^2=8(x+2)$.
View full solution →Find the coordinates of the foci, the vertices, the length of major axis, the eccentricity and the length of the latus rectum of the ellipse : $4 x^2+9 y^2-16 x+54 y+61=0$
View full solution →Find the coordinates of the foci, the vertices, the length of major axis, the eccentricity and the length of the latus rectum of the ellipse : $3 x^2+4 y^2=1$
View full solution →Find the coordinates of the foci, the vertices, the length of major axis, the eccentricity and the length of the latus rectum of the ellipse : $4 x^2+3 y^2=1$
View full solution →Find the equation of the parabola whose diretrix is $x+3=0$
View full solution →Find the equation of an ellipse whose major axis is on the $\mathrm{X}$-axis and passes through the points $(4,3)$ and $(6,2)$
View full solution →Find the length of the latus rectum of the parabola $y^2=4 a x$ passing through the point $(2$,-6).
View full solution →Find the length of transverse axis, length of conjugate axis, the eccentricity, the co-ordinates of foci, equations of directrices and the length of latus rectum of the hyperbola
$\frac{x^2}{4}-\frac{y^2}{12}=1$
$\frac{y^2}{9}-\frac{x^2}{16}=1$
View full solution →