HSC Arts (English Medium) 11th Standard - Maharashtra State Board Question Bank Solutions

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

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

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

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

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

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The equation of the ellipse is 16x² + 25y² = 400. The equations of the tangents making an angle of 180° with the major axis are

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The equation of the tangent to the ellipse 4x² + 9y² = 36 which is perpendicular to the 3x + 4y = 17 is,

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Centre of the ellipse 9x² + 5y² − 36x − 50y − 164 = 0 is at

Find the equation of the ellipse in standard form if the length of major axis 10 and the distance between foci is 8

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Find the equation of the tangent to the ellipse x² + 4y² = 100 at (8, 3)

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The variance of 19, 21, 23, 25, and 27 is 8. The variance of 14, 16, 18, 20, and 22 is:

First 6 faced die which is numbered 1 through 6 is thrown then a 5 faced die which is numbered 1 through 5 is thrown. What is the probability that the sum of the numbers on the upper faces of the dice is divisible by 2 or 3?