Test: Hyperbola- 3 - Commerce MCQ

The equation to the chord joining two points (x₁, y₁) and (x₂, y₂) on the rectangular hyperbola xy = c² is

The equation 9x² - 16y² - 18x + 32y - 15 = 0 represent a hyperbola

From the points of the circle x² + y² = a², tangents are drawn to the hyperbola x² – y² = a²; then the locus of the middle points of the chords of contact is

The tangent to the hyperbola xy = c² at the point P intersects the x-axis at T and the y-axis at T'. The normal to the hyperbola at P intersects the x-axis at N and the y-axis at N'. The areas of the triangles PNT and PNT' are D and D' respectively, then  is

The asymptote of the hyperbola  form with any tangent to the hyperbola a triangle whose area is a² tan l in magnitude then its eccentricity is

From any point on the hyperbola H₁ : (x²/a²) - (y²/b²) = 1 tangents are drawn to the hyperbola .H₂ : (x²/a²) - (y²/b²) = 2. The area cut-off by the chord of contact on the asymptotes of H₂ is equal to

The tangent at P on the hyperbola (x² / a²) - (y² / b²) = 1 meets the asymptote  at Q. If the locus of the mid point of PQ has the equation (x² / a²) - (y² / b²) = k, then k has the value equal to

The tangent to the hyperbola, x² - 3y² = 3 at the point (√3, 0) when associated with two asymptotes constitutes.

If θ is the angle between the asymptotes of the hyperbola with eccentricity e, then sec θ/2 can be

If (5, 12) and (24, 7) are the focii of a conic passing through the origin then the eccentricity of conic is

The point of contact of 5x + 12y = 19 and x² – 9y² = 9 will lie on

Equation (2 + λ)x² - 2λxy + (λ - 1)y² - 4x - 2 = 0 represents a hyperbola if