Conic Section - circle and parabola

If the parabola y² = 4ax passes through the point (3, 2), then the length of its latus rectum is

• 2/3

• 4/3

• 1/3

• 4

The area of the circle centred at (1, 2) and passing through (4, 6) is

• $5\pi$

• $10\pi$

• $25\pi$

• none of these

The equation of the circle with centre (–3, 2) and radius 4.

• $(x+3)^2+(y–2)^2=16$

• $(x\ -3)^2+(y\ +2)^2=16$

• $(x+3)^2+(y\ +2)^2=16$

• none of these

Find the centre and the radius of the circle  $x^2+y^2+8x+10y\ –\ 8=0$  

• centre at (–  4, – 5) and radius 7

• centre at ( 4, – 5) and radius 7

• centre at ( 4, 5) and radius 7

• none of these

The equation of the parabola with focus (2,0) and directrix

x = – 2.

• $y^2=4x$

• $y^2=8x$

• $x^2=4y$

• $x^2=8y$

Find the equation of the parabola which is symmetric about the y-axis, and passes through the point (2,–3).

• $3x^2=–\ 4y$

• $3x^2=4y$

• $3y^2=–\ 4x$

• $3y^2=4x$

The point (–2.5, 3.5) lie ______ the circle x² + y² = 25

• inside

• outside

• on

• none of these