The equation of the circle passing through (1, 5) and (4, 1) and touching y-axis is x² + y² − 5x − 6y + 9 + \(\lambda\)(4x + 3y − 19) = 0 where λ is equal to

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

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

Equation of tangent at (-4, -4) on x² = -4y is _____________

y² - 2x - 2y + 5 = 0 is a _________

The line 3x+4y−12 = 0 meets the coordinate axes at A and B. Find the equation of the circle drawn on AB as diameter.

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

Find centre and radius of the following circles.
2x²+2y²−6x+4y+2 = 0

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

Find the length of the tangent from (2, -3) to the circle x² + y² - 8x - 9y + 12 = 0.

Find the centre and radius of the circle 3x² + (a + 1)y² + 6x − 9y + a + 4 = 0.

Find the equation of the tangent and normal to the circle x²+y²−6x+6y−8 = 0 at (2, 2) .

Find the equation of the hyperbola whose conjugate axis is 5 and the distance between the foci is 13.

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.

On lighting a rocket cracker it gets projected in a parabolic path and reaches a maximum height of 4 m when it is 6 m away from the point of projection. Finally it reaches the ground 12 m away from the starting point. Find the angle of projection.

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.