HSC Science (Computer Science) 11th Standard - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

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

Find the equations of the tangents to the ellipse `x^2/16 + y^2/9` = 1, making equal intercepts on co-ordinate axes

Select the correct option from the given alternatives:

If `"P"(pi/4)` is any point on he ellipse 9x² + 25y² = 225. S and S¹ are its foci then SP.S¹P =

Select the correct option from the given alternatives:

The equation of the ellipse having foci (+4, 0) and eccentricity `1/3` is

Select the correct option from the given alternatives:

The equation of the ellipse having eccentricity `sqrt(3)/2` and passing through (− 8, 3) is

Select the correct option from the given alternatives:

If the line 4x − 3y + k = 0 touches the ellipse 5x² + 9y² = 45 then the value of k is