Parabola - Gujarat Board (GSEB) STD 11 Science MATHS Questions

Q 1MCQ1 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 2MCQ1 Mark

The equation of the parabola whose vertex is $(a, 0)$ and the directrix has the equation $x + y = 3a$, is

A
$x^2+y^2+2 x y+6 a x+10 a y+7 a^2=0$
✓
$x^2-2 x y+y^2+6 a x+10 a y-7 a^2=0$
C
$x^2-2 x y+y^2-6 a x+10 a y-7 a^2=0$
D
None of these

Answer: B.

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Q 3MCQ1 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 4MCQ1 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 5MCQ1 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 6(Each question 1 marks)1 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 7(Each question 1 marks)1 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 8(Each question 1 marks)1 Mark

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

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Q 9(Each question 1 marks)1 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 10(Each question 1 marks)1 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 11(Each question 2 marks)2 Marks

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

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Q 12(Each question 3 marks)3 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 13(Each question 3 marks)3 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 14(Each question 3 marks)3 Marks

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

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Q 15(Each question 3 marks)3 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 16(Each question 3 marks)3 Marks

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

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Q 17(Each question 4 marks)4 Marks

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.

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Q 18(Each question 4 marks)4 Marks

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

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Q 19(Each question 4 marks)4 Marks

Find the equation of the parabola, if The focus is at $(a, 0)$ and the vertex is at $(a', 0)$.

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Q 20(Each question 4 marks)4 Marks

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.

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Q 21(Each question 4 marks)4 Marks

Find the vertex, focus, axis, directrix and latus-rectum of the following parabolas: $4(y - 1)^2 = -7(x - 3)$.

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