The eccentricity of the hyperbola whose latus rectum is 8 and conjugate axis is equal to half the distance between the foci is

The centre of the circle inscribed in a square formed by the lines x² − 8x − 12 = 0 and y² − 14y + 45 = 0 is

If P(x, y) be any point on 16x² + 25y² = 400 with foci F₁ (3, 0) and F₂ (-3, 0) then PF₁  + PF₂ is

If the normals of the parabola y² = 4x drawn at the end points of its latus rectum are tangents to the circle (x − 3)² + (y + 2)² = r² , then the value of r² is

If a parabolic reflector is 20 cm in diameter and 5 cm in diameter and 5 cm deep, then its focus is ____________

If y = 4x + c is a tangent to the circle x² + y² = 9, find c 

Obtain the equation of the circles with radius 5 cm and touching x-axis at the origin in general form.

Obtain the equation of the circle for which (3, 4) and (2, -7) are the ends of a diameter.

Find the locus of a point which divides so that the sum of its distances from (-4, 0) and (4, 0) is 10 units.

Find the equation of the hyperbola whose vertices are (0, ±7) and e = \(\frac { 4 }{ 3 } \)

Find the equations of the tangent and normal to the circle x² + y² = 25 at P(-3, 4).

Find the equation of circles that touch both the axes and pass through (-4, -2) in general form.

Find the equation of the hyperbola with vertices (0, ±4) and foci(0, ±6).

Find the equations of tangent and normal to the ellipse x²+4y² = 32 when \(\theta =\frac { \pi }{ 4 } \)

For the hyperbola 3x² - 6y² = -18, find the length of transverse and conjugate axes and eccentricity.

Find the equation of the ellipse whose eccentricity is \(\frac { 1 }{ 2 } \), one of the foci is(2, 3) and a directrix is x = 7. Also find the length of the major and minor axes of the ellipse.

Find the centre, foci, and eccentricity of the hyperbola 11x² − 25y² −44x + 50y −256 = 0

An equilateral triangle is inscribed in the parabola y² = 4ax whose vertex is at the vertex of the parabola. Find the length of its side.

The foci of a hyperbola coincides with the foci of the ellipse \(\frac { { x }^{ 2 } }{ 25 } +\frac { y^{ 2 } }{ 9 } =1\). Find the equation of the hyperbola if its eccentricity is 2.