Parabola - UP Board (UPMSP) STD 11 Science MATHS Questions

Q 1M.C.Q (1 Marks)1 Mark

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.

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Q 2M.C.Q (1 Marks)1 Mark

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
None of these

Answer: B.

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Q 3M.C.Q (1 Marks)1 Mark

The vertex of the parabola $(y + a)^2 = 8a (x - a)$ is

A
$(-a, -a)$
✓
$(a, -a)$
C
$(-a, a)$
D
None of these

Answer: B.

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Q 4M.C.Q (1 Marks)1 Mark

If $V$ and $S$ are respectively the vertex and focus of the parabola $y^2 + 6y + 2x + 5 = 0,$ then $SV =$

A
$2$
✓
$\frac{1}{2}$
C
$1$
D
None of these

Answer: B.

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Q 5M.C.Q (1 Marks)1 Mark

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
None of these

Answer: A.

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Q 61 Marks Question1 Mark

Write the length of the chord of the parabola $y^2 = 4ax$ which passes through the vertex and is inclined to the axis at $\frac{\pi}{4}.$

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Q 71 Marks Question1 Mark

Write the equation of the parabola whose vertex is at $(-3, 0)$ and the directrix is $x + 5 = 0.$

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Q 81 Marks Question1 Mark

Write the equation of the parabola with focus $(0, 0)$ and directrix $x + y - 4 = 0.$

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Q 91 Marks Question1 Mark

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.

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Q 101 Marks Question1 Mark

Write the coordinates of the vertex of the parabola whose focus is at $(-2, 1)$ and directrix is the line $x + y - 3 = 0.$

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Q 112 Marks Questions2 Marks

Find the vertex, focus, axis, directrix and latus-rectum of the following parabolas:
$y^2 = 8x.$

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Q 123 Marks Question3 Marks

Find the vertex, focus, axis, directrix and latus-rectum of the following parabolas:
$y^2 - 4y - 3x + 1 = 0.$

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Q 133 Marks Question3 Marks

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.

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Q 143 Marks Question3 Marks

At what point of the parabola $x^2 = 9y$ is the abscissa three times that of ordinate$?$

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Q 153 Marks Question3 Marks

Find the equation of a parabola with vertex at the origin, the axis along x-axis and passing through (2, 3).

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Q 163 Marks Question3 Marks

Find the equation of the parabola whose focus is $(5, 2)$ and having vertex at $( 3, 2).$

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Q 175 Marks Questions5 Marks

Find the vertex, focus, axis, directrix and latus-rectum of the following parabolas:
$y^2 = 5x - 4y - 9.$

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Q 185 Marks Questions5 Marks

Find the equation of the parabola whose:
Focus is (0, 0) and the directrix 2 x - y + 1 = 0

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Q 195 Marks Questions5 Marks

Find the vertex, focus, axis, directrix and latus-rectum of the following parabolas:
$y^2 + 4x + 4y - 3 = 0$

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Q 205 Marks Questions5 Marks

Find the vertex, focus, axis, directrix and latus-rectum of the following parabolas:
$x^2 + y = 6x - 14.$

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Q 215 Marks Questions5 Marks

If the points (O, 4) and(O, 2) are respectively the vertex and focus of a parabola, then find the equation of the parabola.

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