If a chord of the parabola y = 4x passes through its focus and makes an angle 0 with the X-axis, then its length is

• $4{\cos }^2\left(\mathrm{\theta }\right)$

• $4{\sin }^2\left(\mathrm{\theta }\right)$

• $4{\csc }^2\left(\mathrm{\theta }\right)$

• $4{\sec }^2\left(\mathrm{\theta }\right)$

If the straight line y = mx + c is parallel to the axis of the parabola y = bx and intersects the parabola at $\left(\frac{{\mathrm{c}}^2}{8}, \mathrm{c}\right)$, then the length of the latus rectum is

• 2

• 3

• 4

• 8

The eccentricity of the ellipse x² + 4y² + 2x + 16y + 13 = 0 is

• $\frac{\sqrt{3}}{2}$

• $\frac{1}{2}$

• $\frac{1}{\sqrt{3}}$

• $\frac{1}{\sqrt{2}}$

The angle between the asymptotes of the hyperbola x² - 3y² = 3 is

• $\frac{\mathrm{\pi }}{6}$

• $\frac{\mathrm{\pi }}{4}$

• $\frac{\mathrm{\pi }}{3}$

• $\frac{\mathrm{\pi }}{2}$

If the area of the triangle formed by the pair of lines 8x² - 6xy + y² = 0 and the line 2x + 3y = a is 7, then a is equal to

• 14

• $14\sqrt{2}$

• $28\sqrt{2}$

• 28

If the line x + 3y = 0 is the tangent at (0, 0) to the circle of radius 1, then the centre of one such circle is

• (3, 0)

• $\left(\frac{- 1}{\sqrt{10}}, \frac{3}{\sqrt{10}}\right)$

• $\left(\frac{3}{\sqrt{10}}, \frac{- 3}{\sqrt{10}}\right)$

• $\left(\frac{1}{\sqrt{10}}, \frac{3}{\sqrt{10}}\right)$

A circle passes through the point (3, 4) and cuts the circle x² + y² = a² orthogonally; the locus of its centre is a straight line. If the distance of this straight line from the origin is 25, then a is equal to

• 250

• 225

• 100

• 25

The equation to the line joining the centres of the circles belonging to the coaxial system of circles 4x² + 4y² - 12x + 6y - 3 + $\mathrm{\lambda }$(x + 2y - 6) = 0 is

• 8x - 4y - 15 = 0

• 8x - 4y + 15 = 0

• 3x - 4y - 5 = 0

• 3x - 4y + 5 = 0

Let x + y = k be a normal to the parabola y² = 12x. If p is length of the perpendicular from the focus of the parabola onto this normal, then 4k - 2p² is equal to

• 1

• 0

• - 1

• 2

550.

If the line 2x + 5y = 12 intersects the ellipse 4x² + 5y² = 20 in two distinct points A and B,then mid-point of AB is

• (0, 1)

• (1, 2)

• (1, 0)

• (2, 1)