HSC Science (Computer Science) इयत्ता ११ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Find length of latus rectum of the parabola y² = 4ax passing through the point (2, –6)

Find the area of the triangle formed by the line joining the vertex of the parabola x² = 12y to the end points of latus rectum.

If a parabolic reflector is 20 cm in diameter and 5 cm deep, find its focus.

Find coordinate of focus, vertex and equation of directrix and the axis of the parabola y = x² – 2x + 3

Find the equation of tangent to the parabola y² = 12x from the point (2, 5)

Find the equation of tangent to the parabola y² = 36x from the point (2, 9)

If the tangent drawn from the point (–6, 9) to the parabola y² = kx are perpendicular to each other, find k

Two tangents to the parabola y² = 8x meet the tangents at the vertex in the point P and Q. If PQ = 4, prove that the equation of the locus of the point of intersection of two tangent is y² = 8(x + 2).

Find the equation of common tangent to the parabola y² = 4x and x² = 32y

Find the equation of the locus of a point, the tangents from which to the parabola y² = 18x are such that some of their slopes is –3

The tower of a bridge, hung in the form of a parabola have their tops 30 meters above the roadway and are 200 meters apart. If the cable is 5 meters above the roadway at the centre of the bridge, find the length of the vertical supporting cable 30 meters from the centre.

A circle whose centre is (4, –1) passes through the focus of the parabola x² + 16y = 0.

Show that the circle touches the directrix of the parabola.

Select the correct option from the given alternatives:

The line y = mx + 1 is a tangent to the parabola y² = 4x, if m is _______

Select the correct option from the given alternatives:

The length of latus rectum of the parabola x² – 4x – 8y + 12 = 0 is _________

Select the correct option from the given alternatives:

If the focus of the parabola is (0, –3) its directrix is y = 3 then its equation is

Select the correct option from the given alternatives:

The coordinates of a point on the parabola y² = 8x whose focal distance is 4 are _______

Select the correct option from the given alternatives:

The endpoints of latus rectum of the parabola y² = 24x are _______

Select the correct option from the given alternatives:

Equation of the parabola with vertex at the origin and directrix x + 8 = 0 is __________

Select the correct option from the given alternatives:

The area of the triangle formed by the line joining the vertex of the parabola x² = 12y to the endpoints of its latus rectum is _________

Select the correct option from the given alternatives:

The equation of the parabola having (2, 4) and (2, –4) as endpoints of its latus rectum is _________