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

The equation of the normal to the circle x² + y² − 2x − 2y + 1 = 0 which is parallel to the line 2x + 4y = 3 is

If x + y = k is a normal to the parabola y² = 12x, then the value of k is

y² - 2x - 2y + 5 = 0 is a _________

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

Find the equation of the circle with centre (2, -1) and passing through the point (3, 6) in standard form.

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

Find the equation of tangent to the circle x² +y² + 2x - 3y - 8 = 0 at (2, 3).

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 eccentricity of the hyperbola with foci on the x-axis if the length of its conjugate axis is \({ \left( \frac { 3 }{ 4 } \right) }^{ th }\) of the length of its tranverse axis.

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 area of th triangle found by the lines Joining the vertex of the parabola x² = -36y to the ends of the latus rectum.

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

Find the value of c if y = x + c is a tangent to the hyperbola 9x² - 16y² = 144.

Find the vertex, focus, directrix, and length of the latus rectum of the parabola x²−4x−5y−1 = 0.

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.

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.

A kho-kho player In a practice session while running realises that the sum of tne distances from the two kho-kho poles from him is always 8m. Find the equation of the path traced by him of the distance between the poles is 6m.