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

• circle

• straight line

• parabola

• ellipse

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 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)

The locus of the middle points of all chords of the parabola y² = 4ax passing through the vertex is

• a straight line

• an ellipse

• a parabola

• a circle

Prove that the centre of the smallest circle passing through origin and whose centre lies on y = x + 1 is $\left(- \frac{1}{2}, \frac{1}{2}\right)$

If t₁ and t₂ be the parameters of the end points of a focal chord for the parabola y² = 4ax, then which one is true?

• t₁t₂ = 1

• $\frac{{\mathrm{t}}_1}{{\mathrm{t}}_2} = 1$

• t₁t₂ = - 1

• t₁ + t₂ = - 1

110.

S and T are the foci of an ellipse and B is end point of the minor axis. If STB is an equilateral triangle, the eccentricity of the ellipse is

• $\frac{1}{4}$

• $\frac{1}{3}$

• $\frac{1}{2}$

• $\frac{2}{3}$