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Nakul Pratap Barad

Asked: 3 years agoIn: Parabola

The eccentricity of the hyperbola \(\rm \frac{x^2}{100} – \frac{y^2}{75} = 1\) is
1. \(\sqrt { \frac{3}{4}}\)
2. \(\sqrt { \frac{5}{4}}\)
3. \(\sqrt { \frac{7}{4}}\)
4. \(\sqrt { \frac{7}{3}}\)

Tanay Pratap Devi

Asked: 3 years agoIn: Parabola

Find the director circle of the parabola x² + 2y = 4x – 3 .

Meghana Aggarwal

Asked: 3 years agoIn: Parabola

The parametric coordinate of any point of the parabola y² = 4ax is
1. (at², 2at)
2. (-at², 2at)
3. (a sin2 t, -2a sin t)
4. None of these

Giaan Badami

Asked: 3 years agoIn: Parabola

The equation of the hyperbola with center at the origin, length of the transverse axis is 6 and one focus at (0, 4) is ?
1. \(\rm \frac {y^2} 7 – \frac {x^2} 9 = 1\)
2. \(\rm \frac {y^2} 9 – \frac {x^2} 7 = 1\)
3. \(\rm \frac {y^2} 9 + \frac {x^2} 9 = 1\)
4. \(\rm \frac {y^2} 7 + \frac {x^2} 9 = 1\)

Navami Dixit

Asked: 3 years agoIn: Parabola

Equation of the normal at t is
tx + y = 2at + at³

Tanay Gajendra Panchal

Asked: 3 years agoIn: Parabola

If (x₁, y₁) and (x₂, y₂) are two points on the parabola y₂ = 8x, at which the normals to the curve intersect on the curve, then
(A) x₁ x₂ = 8
(B) y₁ y₂ = 16
(C) y₁ y₂ = 32
(D) x₁ x₂ = 16

Somnath Sumit Kabra

Asked: 3 years agoIn: Parabola

Find the equation of the hyperbola whose foci are (± 5, 0) and the conjugate axis is of length 8 ?
1. \(\frac{{{x^2}}}{{{9}}} – \frac{{{y^2}}}{{{16}}} = 1\)
2. \(\frac{{{x^2}}}{{{9}}} – \frac{{{y^2}}}{{{7}}} = 1\)
3. \(\frac{{{x^2}}}{{{25}}} – \frac{{{y^2}}}{{{16}}} = 1\)
4. None of these

Rosey Devi

Asked: 3 years agoIn: Parabola

Passage: For the parabola y² = 4ax, the vertex is (0, 0), the focus is (a, 0) and the directrix is x + a = 0.
Answer the following three questions.
(i) The vertex of the parabola (y – 1)² = 2(x – 1) is
(A) (1,0)
(B) (2,0)
(C) (1,1)
(D) (0,1)
(ii) Focus of the parabola y² = 4(x – 1) is
(A) (1, 0)
(B) (2, 0)
(C) (1, 1)
(D) (2, 2)
(iii) The directrix of the parabola (y – 2)² = 4(x – 1)
(A) x = 1
(B) x = -1
(C) x = 2
(D) x = 0

Rimi Som

Asked: 3 years agoIn: Parabola

Prove that the circumcircle of a triangle formed by three tangents to a parabola passes through the focus of the parabola.

Madhavi Gagrani

Asked: 3 years agoIn: Parabola

What is the equation of the ellipse having foci (±2,0) and the eccentricity 1/2
1. \(\rm \frac{x^2}{6}-\frac{y^2}{16}=1\)
2. \(\rm \frac{x^2}{12}+\frac{y^2}{16}=1\)
3. \(\rm \frac{x^2}{16}+\frac{y^2}{12}=1\)
4. \(\rm \frac{x^2}{4}+\frac{y^2}{144}=1\)

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Parabola

The eccentricity of the hyperbola \(\rm \frac{x^2}{100} – \frac{y^2}{75} = 1\) is
1. \(\sqrt { \frac{3}{4}}\)
2. \(\sqrt { \frac{5}{4}}\)
3. \(\sqrt { \frac{7}{4}}\)
4. \(\sqrt { \frac{7}{3}}\)

Find the director circle of the parabola x² + 2y = 4x – 3 .

The parametric coordinate of any point of the parabola y² = 4ax is
1. (at², 2at)
2. (-at², 2at)
3. (a sin2 t, -2a sin t)
4. None of these

Equation of the normal at t is
tx + y = 2at + at³

If (x₁, y₁) and (x₂, y₂) are two points on the parabola y₂ = 8x, at which the normals to the curve intersect on the curve, then
(A) x₁ x₂ = 8
(B) y₁ y₂ = 16
(C) y₁ y₂ = 32
(D) x₁ x₂ = 16

Find the equation of the hyperbola whose foci are (± 5, 0) and the conjugate axis is of length 8 ?
1. \(\frac{{{x^2}}}{{{9}}} – \frac{{{y^2}}}{{{16}}} = 1\)
2. \(\frac{{{x^2}}}{{{9}}} – \frac{{{y^2}}}{{{7}}} = 1\)
3. \(\frac{{{x^2}}}{{{25}}} – \frac{{{y^2}}}{{{16}}} = 1\)
4. None of these

Prove that the circumcircle of a triangle formed by three tangents to a parabola passes through the focus of the parabola.

What is the equation of the ellipse having foci (±2,0) and the eccentricity 1/2
1. \(\rm \frac{x^2}{6}-\frac{y^2}{16}=1\)
2. \(\rm \frac{x^2}{12}+\frac{y^2}{16}=1\)
3. \(\rm \frac{x^2}{16}+\frac{y^2}{12}=1\)
4. \(\rm \frac{x^2}{4}+\frac{y^2}{144}=1\)

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