Sample QuestionsParabola questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
The line $2x - y + 4 = 0$ cuts the parabola $y^2 = 8x$ in $P$ and $Q$. The mid$-$point of $PQ$ is
- A
$(1, 2)$
- B
$(1, -2)$
- ✓
$(-1, 2)$
- D
$(-1, -2)$
Answer: C.
View full solution →The equation of the parabola whose vertex is $(a, 0)$ and the directrix has the equation $x + y = 3a,$ is
- A
$x^2 + y^2 + 2xy + 6ax + 10ay + 7a^2 = 0$
- ✓
$x^2 - 2xy + y^2 + 6ax + 10ay - 7a^2 = 0$
- C
$x^2 - 2xy + y^2 - 6ax + 10ay - 7a^2 = 0$
- D
Answer: B.
View full solution →The vertex of the parabola $(y + a)^2 = 8a (x - a)$ is
- A
$(-a, -a)$
- ✓
$(a, -a)$
- C
$(-a, a)$
- D
Answer: B.
View full solution →If $V$ and $S$ are respectively the vertex and focus of the parabola $y^2 + 6y + 2x + 5 = 0$, then $SV =$
Answer: B.
View full solution →The coordinates of the focus of the parabola $y^2 - x - 2y + 2 = 0$ are
- ✓
$\Big(\frac{5}{4}, 1\Big)$
- B
$\Big(\frac{1}{4}, 0\Big)$
- C
$(1, 1)$
- D
Answer: A.
View full solution →Write the length of the chord of the parabola $y^2 = 4ax $which passes through the vertex and is inclined to the axis at $\frac{\pi}{4}.$
View full solution →Write the equation of the parabola whose vertex is at $(-3, 0)$ and the directrix is $x + 5 = 0$.
View full solution →Write the equation of the parabola with focus $(0, 0)$ and directrix $x + y - 4 = 0$.
View full solution →If the coordinates of the vertex and focus of a parabola are $(-1, 1)$ and $(2, 3)$ respectively, then write the equation of its directrix.
View full solution →Write the coordinates of the vertex of the parabola whose focus is at $(-2, 1)$ and directrix is the line $x + y - 3 = 0$.
View full solution →Find the vertex, focus, axis, directrix and latus-rectum of the following parabolas:
$y^2 = 8x.$
View full solution →Find the vertex, focus, axis, directrix and latus-rectum of the following parabolas:
$y^2 - 4y - 3x + 1 = 0.$
View full solution →Find the length of the line segment joining the vertex of the parabola $y^2 = 4ax$ and a point on the parabola where the line-segment makes an angle $\theta$ to the x-axis.
View full solution →At what point of the parabola $x^2 = 9y$ is the abscissa three times that of ordinate?
View full solution →Find the equation of a parabola with vertex at the origin, the axis along x-axis and passing through (2, 3).
Find the equation of the parabola whose focus is $(5, 2)$ and having vertex at $( 3, 2)$.
View full solution →Find the vertex, focus, axis, directrix and latus-rectum of the following parabolas:
$y^2 = 5x - 4y - 9.$
View full solution →Find the equation of the parabola whose:
Focus is (0, 0) and the directrix 2 x - y + 1 = 0
Find the vertex, focus, axis, directrix and latus-rectum of the following parabolas:
$y^2 + 4x + 4y - 3 = 0$
View full solution →Find the vertex, focus, axis, directrix and latus-rectum of the following parabolas:
$x^2 + y = 6x - 14.$
View full solution →If the points (O, 4) and(O, 2) are respectively the vertex and focus of a parabola, then find the equation of the parabola.
Find the equation of the parabola, if
The focus is at (0, 0) and vertex is at the intersection of the lines x + y = 1 and x - y = 3.
Find the vertex, focus, axis, directrix and latus-rectum of the following parabolas:
$y^2 = 8x + 8y.$
View full solution →Find the equation of the parabola, if
The focus is at $(a, 0$) and the vertex is at $(a', 0).$
View full solution →Find the coordinates of the point of intersection of the axis and the directrix of the parabola whose focus is (3, 3) and directrix is 3x - 4y = 2. Find also the length of the latus-rectum.
Find the vertex, focus, axis, directrix and latus-rectum of the following parabolas:
$4(y - 1)^2 = -7(x - 3).$
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