Arts (English Medium) कक्षा ११ - CBSE Question Bank Solutions

Write the eccentricity of the hyperbola whose latus-rectum is half of its transverse axis.

If the latus-rectum through one focus of a hyperbola subtends a right angle at the farther vertex, then write the eccentricity of the hyperbola.

The latus-rectum of the hyperbola 16x² − 9y² = 144 is

Find the equation of the circle with:

Centre (−2, 3) and radius 4.

Find the equation of the circle with:

Centre (a, b) and radius\[\sqrt{a^2 + b^2}\]

Find the equation of the circle with:

Centre (0, −1) and radius 1.

Find the equation of the circle with:

Centre (a cos α, a sin α) and radius a.

Find the equation of the circle with:

Centre (a, a) and radius \[\sqrt{2}\]a.

Find the centre and radius of each of the following circles:

 (x − 1)² + y² = 4

Find the centre and radius of each of the following circles:

(x + 5)² + (y + 1)² = 9

Find the centre and radius of each of the following circles:

x² + y² − 4x + 6y = 5

Find the centre and radius of each of the following circles:

x² + y² − x + 2y − 3 = 0.

Find the equation of the circle passing through the point of intersection of the lines x + 3y = 0 and 2x − 7y = 0 and whose centre is the point of intersection of the lines x + y + 1 = 0 and x − 2y + 4 = 0.

If the equations of two diameters of a circle are 2x + y = 6 and 3x + 2y = 4 and the radius is 10, find the equation of the circle.

Find the equation of a circle
which touches both the axes at a distance of 6 units from the origin.

Find the equation of a circle which touches x-axis at a distance 5 from the origin and radius 6 units.

Find the equation of a circle
which touches both the axes and passes through the point (2, 1).