Mathematics : Conic Section

If the normal at (ap, 2ap) on the parabola y² = 4ax, meets the parabola again at (aq² , 2aq), then

• p² + pq + 2 = 0

• p² - pq + 2 = 0

• q² + pq + 2 = 0

• p² + pq + 1

The curve described parametrically by x = t² + 2t - 1, y = 3t + 5 represents :

• an ellipse

• a hyperbola

• a parabola

• a circle

From the point P (16, 7), tangents PQ and PR are drawn to the circle x² + y² - 2x - 4y - 20 = 0. If C is the centre of the circle, then area of the quadrilateral PQCR is

• 15 sq unit

• 50 sq unit

• 75 sq unit

• 150 sq unit

Tangents are drawn from any point of the circle x² + y² = a² to the circle x² + y² = b². If the chord of contact touches the circle x² + y² = c², then

• a, b, c are in AP

• a, b, c are in GP

• a, b, c are in HP

• a, b, c are in GP

The equation of tangents to the circle x² + y² = 4, which are parallel to x + 2y + 3 = 0, are

• $\mathrm{x} + 2\mathrm{y} = \pm 2\sqrt{3}$

• $\mathrm{x} - 2\mathrm{y} = \pm 2\sqrt{5}$

• $\mathrm{x} - 2\mathrm{y} = \pm 2\sqrt{3}$

• $\mathrm{x} + 2\mathrm{y} = \pm 2\sqrt{5}$

Equation of the circle, which passes through (4, 5) and whose centre is (2, 2), is

• x² + y² + 4x + 4y - 5 = 0

• x² + y² - 4x - 4y - 5 = 0

• x² + y² - 4x = 13

• x² + y² - 4x - 4y + 5 = 0

If one end of diameter of a circle x² + y² - 4x - 6y + 11 = 0 is (3, 4), then the other end is

• (0, 0)

• (1, 1)

• (1, 2)

• (2, 1)

Equation of the circle which passes through the points (3, - 2) and (- 2, 0) and whose centre lies on the line 2x - y - 3 = 0 , is

• x² + y² - 3x - 12y + 2 = 0

• x² + y² - 3x + 12y + 2 = 0

• x² + y² + 3x + 12y + 2 = 0

• x² + y² - 3x - 12y - 2 = 0

If the circle x² + y² + 2gx + 2fy + c = 0 touches X-axis, then

• g = f

• g² = c

• f² = c

• g² + f² = c

The end points of latusrectum of parabola x² + 8y = 0 are

• (- 4, - 2) and (4, 2)

• (4, - 2) and (- 4, 2)

• (- 4, - 2) and (4, - 2)

• (4, 2) and (- 4, 2)