Arts (English Medium) Class 12 - CBSE Question Bank Solutions for Mathematics

The equation of the normal to the curve y = x + sin x cos x at x = `π/2` is ___________ .

The equation of the normal to the curve y = x(2 − x) at the point (2, 0) is ________________ .

The point on the curve y² = x where tangent makes 45° angle with x-axis is ______________ .

If the tangent to the curve x = a t², y = 2 at is perpendicular to x-axis, then its point of contact is _____________ .

The point on the curve y = x² − 3x + 2 where tangent is perpendicular to y = x is ________________ .

The point on the curve y² = x where tangent makes 45° angle with x-axis is ____________________ .

The point at the curve y = 12x − x² where the slope of the tangent is zero will be _____________ .

The angle between the curves y² = x and x² = y at (1, 1) is ______________ .

The equation of the normal to the curve 3x² − y² = 8 which is parallel to x + 3y = 8 is ____________ .

The equations of tangent at those points where the curve y = x² − 3x + 2 meets x-axis are _______________ .

The slope of the tangent to the curve x = t² + 3 t − 8, y = 2t² − 2t − 5 at point (2, −1) is ________________ .

At what point the slope of the tangent to the curve x² + y² − 2x − 3 = 0 is zero

The angle of intersection of the curves xy = a² and x² − y² = 2a² is ______________ .

If the curve ay + x² = 7 and x³ = y cut orthogonally at (1, 1), then a is equal to _____________ .

If the line y = x touches the curve y = x² + bx + c at a point (1, 1) then _____________ .

The slope of the tangent to the curve x = 3t² + 1, y = t³ −1 at x = 1 is ___________ .

The curves y = ae^x and y = be^−x cut orthogonally, if ___________ .

The equation of the normal to the curve x = a cos³ θ, y = a sin³ θ at the point θ = π/4 is __________ .

If the curves y = 2 e^x and y = ae^−x intersect orthogonally, then a = _____________ .

The point on the curve y = 6x − x² at which the tangent to the curve is inclined at π/4 to the line x + y= 0 is __________ .