Mathematics : Conic Section

If the line 3x - 2y + p = 0 is normal to the circle x² + y² = 2x - 4y - 1, then p will be

• - 5

• 7

• - 7

• 5

If the two circles x² + y² = r² and x² + y² - 10x + 16 = 0 intersect at two real points, then

• 1 < r < 7

• 3 < r < 10

• 2 < r < 9

• 2 < r < 8

The equation of the common tangent to the parabolas y² = 2x and x² = 16y will be

• x + y + 2 = 0

• x - 3y + 1 = 0

• x + 2y - 2 = 0

• x + 2y + 2 = 0

The equation of the tangent to the parabola y² = 8x, which is parallel to the line 2x - y + 7 = 0, will be

• y = x + 1

• y = 2x + 1

• y = 3x + 1

• y = 4x + 1

The distance of a point on ellipse $\frac{{\mathrm{x}}^2}{6} + \frac{{\mathrm{y}}^2}{2} = 1$ from its centre is 2. The eccentric angle of the point will be

• $\frac{\mathrm{\pi }}{4} \mathrm{or} \frac{\mathrm{\pi }}{3}$

• $\frac{\mathrm{\pi }}{3} \mathrm{or} \frac{3\mathrm{\pi }}{5}$

• $\frac{\mathrm{\pi }}{4} \mathrm{or} \frac{3\mathrm{\pi }}{4}$

• None of these

The distance between the foci of a hyperbola is 16 and its eccentncity is $\sqrt{2}$. Its equation will be

• x² - y² = 1

• x² - y² = 20

• x² - y² = 4

• x² - y² = 32

Equation of the circle which passes through the origin and cuts intercepts of lengths a and b on axes is

• x² + y² + ax + by = 0

• x² + y² + ax - by = 0

• x² + y² + bx + ay = 0

• None of the above

If focus ofa parabolais at (3, 3) and its directrix is 3x - 4y = 2, then its latusrectum is

• 2

• 3

• 4

• 5

If the straight line y = 4x + c is a tangent to the ellipse $\frac{{\mathrm{x}}^2}{8} + \frac{{\mathrm{y}}^2}{4} = 1$, then c will be equal to

• $\pm 4$

• $\pm 6$

• $\pm 1$

• $\pm \sqrt{132}$

The distance between the foci of a hyperbola is 16 and its eccentricity is - 2. Its equation will be

• x² - y² = 32

• y² - x² = 32

• x² - y² = 16

• y² - x² = 16