HSC Science (Computer Science) इयत्ता ११ वी - Maharashtra State Board Question Bank Solutions

Find the eccentricity of an ellipse, if the length of its latus rectum is one-third of its minor axis.

Find the eccentricity of an ellipse if the distance between its directrix is three times the distance between its foci

Show that the product of the lengths of the perpendicular segments drawn from the foci to any tangent line to the ellipse `x^2/25 + y^2/16` = 1 is equal to 16

A tangent having slope `–1/2` to the ellipse 3x² + 4y² = 12 intersects the X and Y axes in the points A and B respectively. If O is the origin, find the area of the triangle

Show that the line x – y = 5 is a tangent to the ellipse 9x² + 16y² = 144. Find the point of contact

Show that the line 8y + x = 17 touches the ellipse x² + 4y² = 17. Find the point of contact

Determine whether the line `x + 3ysqrt(2)` = 9 is a tangent to the ellipse `x^2/9 + y^2/4` = 1. If so, find the co-ordinates of the pt of contact

Find k, if the line 3x + 4y + k = 0 touches 9x² + 16y² = 144

Find the equation of the tangent to the ellipse `x^2/5 + y^2/4` = 1 passing through the point (2, –2)

Find the equation of the tangent to the ellipse 4x² + 7y² = 28 from the point (3, –2).

Find the equation of the tangent to the ellipse 2x² + y² = 6 from the point (2, 1).

Find the equation of the tangent to the ellipse x² + 4y² = 9 which are parallel to the line 2x + 3y – 5 = 0.

Find the equation of the tangent to the ellipse `x^2/25 + y^2/4` = 1 which are parallel to the line x + y + 1 = 0.

Find the equation of the tangent to the ellipse 5x² + 9y² = 45 which are ⊥ to the line 3x + 2y + y = 0.

Find the equation of the tangent to the ellipse x² + 4y² = 20, ⊥ to the line 4x + 3y = 7.

Find the equation of the locus of a point the tangents form which to the ellipse 3x² + 5y² = 15 are at right angles

Tangents are drawn through a point P to the ellipse 4x² + 5y² = 20 having inclinations θ₁ and θ₂ such that tan θ₁ + tan θ₂ = 2. Find the equation of the locus of P.

Show that the locus of the point of intersection of tangents at two points on an ellipse, whose eccentric angles differ by a constant, is an ellipse

P and Q are two points on the ellipse `x^2/"a"^2 + y^2/"b"^2` = 1 with eccentric angles θ₁ and θ₂. Find the equation of the locus of the point of intersection of the tangents at P and Q if θ₁ + θ₂ = `π/2`.

The eccentric angles of two points P and Q the ellipse 4x² + y² = 4 differ by `(2pi)/3`. Show that the locus of the point of intersection of the tangents at P and Q is the ellipse 4x² + y² = 16