Conic Section T...

If a normal chord at a point on the parabola y² = 4ax subtends a right angle at the vertex, then t equals

The slopes of the focal chords of the parabola y² = 32x, which are tangents to the circle x² + y² = 4 are

The two curves x³ - 3xy² + 2 = 0 and 3x²y - y³ - 2 = 0, is

Let PQ be a focal chord of the parabola y² = 4ax. The tangents to the parabola at P and Q meet a point lying y = 2x + a, a > 0.
length of chord PQ is

Let PQ be a focal chord of the parabola y² = 4ax. The tangents to the parabola at P and Q meet a point lying y = 2x + a, a > 0.
If chord PQ students an angle θ at the vertex of y² = 4ax, then tan θ is equal to

A circle, 2x² + 2y² = 5 and a parabola, y² = 4√5x.
Statement I An equation of a common tangent to these curve is y = x + √5.
Statement II If the line, y = mx + √5/m (m ≠ 0) is the common tangent, the m satisfies m⁴ - 3m² + 2 = 0.

The line 2x + y + k = 0 is a normal to the parabola y² = -8x, if k is equal to

The values of m, for which the line y = mx + 2 is a tangent to the hyperbola 4x² - 9y² = 36 are