The eccentricity of the hyperbola 4x² - 9y² = 36 is

• $\frac{\sqrt{11}}{3}$

• $\frac{\sqrt{15}}{3}$

• $\frac{\sqrt{13}}{3}$

• $\frac{{\displaystyle \sqrt{14}}}{{\displaystyle 3}}$

The length of the latus rectum of the ellipse 16x² + 25y² = 400 is

• 5/16 unit

• 32/5 unit

• 16/5 unit

• 5/32 unit

The vertex of the parabola y² + 6x - 2y + 13 = 0 is

• (1, - 1)

• (- 2, 1)

• $\left(\frac{3}{2}, 1\right)$

• $\left(- \frac{7}{2}, 1\right)$

The coordinates of a moving point P are (2t² + 4, 4t + 6). Then, its locus will be

• circle

• straight line

• parabola

• ellipse

5.

The equation 8x² + 12y² - 4x + 4y - 1 = 0 represents

• an ellipse

• a hyperbola

• a parabola

• a circle

If the straight line y = mx lies outside the circle x² + y² - 20y + 90 = 0, then the value of m will satisfy

• m < 3

• $\left|\mathrm{m}\right| < 3$

• m > 3

• $\left|\mathrm{m}\right| > 3$

The locus of the passes through (a, 0), (- a, 0) is the centre of a circle which two variable points

• x = 1

• x + y = a

• x + y = 2a

• x = 0

The coordinates of the two points lying on x + y = 4 and at a unit distance from the straight line 4x + 3y = 10 are

• (- 3, 1), (7, 11)

• (3, 1), (- 7, 11)

• (3, 1), (7, 11)

• (5, 3), (- 1, 2)

The intercept on the line y = x by the circle x² = y² - 2x = 0 is AB. Equation of the circle with AB as the diameter is

• x² + y² = 1

• x(x - 1) + y(y - 1) = 0

• x² + y² = 2

• (x - 1)(x - 2) + (y - 1)(y - 2) = 0

If the coordinates of one end of a diameter of the circle x2 + y² + 4x-8y + 5 = 0 are (2, 1), the coordinates of the other end are

• (- 6, - 7)

• (6 , 7)

• (- 6, 7)

• (7, - 6)