31.

What is the radius of the circle passing through the point (2, 4) and having centre at the intersection of the lines x - y = 4 and 2x + 3y + 70 = 0 ?

• 3 units

• 5 units

• 3$\sqrt{3}$ units

• 5$\sqrt{2}$

What is the equation of the hyperbola having latus rectum and eccentricity 8 and $\frac{3}{\sqrt{5}}$ respectively.

• $\frac{{\mathrm{x}}^2}{25} - \frac{{\mathrm{y}}^2}{20} = 1$

• $\frac{{\mathrm{x}}^2}{40} - \frac{{\mathrm{y}}^2}{20} = 1$

• $\frac{{\mathrm{x}}^2}{40} - \frac{{\mathrm{y}}^2}{30} = 1$

• $\frac{{\mathrm{x}}^2}{30} - \frac{{\mathrm{y}}^2}{25} = 1$

If the ellipse 9x² + 16y² = 144 intercepts the line 3x + 4y = 12, then what is the length of the chord so formed ?

• 5 units

• 6 units

• 8 units

• 10 units

What is the eccentricity of rectangular hyperbola ?

• $\sqrt{2}$

• $\sqrt{3}$

• $\sqrt{5}$

• $\sqrt{6}$

What is the curve which passes through the point (1, 1) and whose slope is $\frac{2\mathrm{y}}{\mathrm{x}}$ ?

• Circle

• Parabola

• Ellipse

• Hyperbola

Consider the parabola y = x² + 7x + 2 and the straight liney = 3x - 3.

What are the coordinates of the point on the parabola which is closest to the straight line ?

• (0, 2)

• ( - 2,  - 8)

• ( - 7, 2)

• (1, 10)

Consider the parabola y = x² + 7x + 2 and the straight liney = 3x - 3.

What is the shortest distance from the above point on the parabola to the line ?

• $\frac{\sqrt{10}}{2}$

• $\frac{\sqrt{10}}{5}$

• $\frac{1}{\sqrt{10}}$

• $\frac{\sqrt{5}}{4}$

If the angle between the lines joining the end points of minor axis of the ellipse $\frac{{\mathrm{x}}^2}{{\mathrm{a}}^2} + \frac{{\mathrm{y}}^2}{{\mathrm{b}}^2} = 1$ with one of its foci is $\frac{\mathrm{\pi }}{2}$, then what is the eccentricity of the ellipse ?

• $\frac{1}{2}$

• $\frac{1}{\sqrt{2}}$

• $\frac{\sqrt{3}}{2}$

• $\frac{1}{2\sqrt{2}}$

In the parabola, y² = x, what is the length of the chord passing through the vertex and inclined to the x-axis at an angle θ ?

• sin(θ) . sec²(θ)

• cos(θ) . cosec²(θ)

• cot(θ) . sec²(θ)

• 2tan(θ) . cosec²(θ)

Let P(x, y) be any point on theellipse 25x² + 16y² = 400. If Q(0, 3) and R(0, - 3) are two points, then what is (PQ + PR)

• 12

• 10

• 8

• 6