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

Find the equation of the normal lines to the curve 3x² – y² = 8 which are parallel to the line x + 3y = 4.

At what points on the curve x² + y² – 2x – 4y + 1 = 0, the tangents are parallel to the y-axis?

Show that the line `x/"a" + y/"b"` = 1, touches the curve y = b · e^– x/a at the point where the curve intersects the axis of y

If the straight line x cosα + y sinα = p touches the curve `x^2/"a"^2 + y^2/"b"^2` = 1, then prove that a² cos²α + b² sin²α = p².

The curve y = `x^(1/5)` has at (0, 0) ______.

The equation of normal to the curve 3x² – y² = 8 which is parallel to the line x + 3y = 8 is ______.

If the curve ay + x² = 7 and x³ = y, cut orthogonally at (1, 1), then the value of a is ______.

The equation of tangent to the curve y(1 + x²) = 2 – x, where it crosses x-axis is ______.

The points at which the tangents to the curve y = x³ – 12x + 18 are parallel to x-axis are ______.

The tangent to the curve y = e^2x at the point (0, 1) meets x-axis at ______.

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

The two curves x³ – 3xy² + 2 = 0 and 3x²y – y³ – 2 = 0 intersect at an angle of ______.

The equation of normal to the curve y = tanx at (0, 0) is ______.

Find the differential equation of the family of curves y = Ae^2x + B.e^–2x.

Find the differential equation of the family of lines through the origin.

Find the equation of a curve whose tangent at any point on it, different from origin, has slope `y + y/x`.

Find the equation of a curve passing through the point (1, 1) if the perpendicular distance of the origin from the normal at any point P(x, y) of the curve is equal to the distance of P from the x-axis.

The solution of the differential equation `2x * "dy"/"dx" y` = 3 represents a family of ______.

The differential equation representing the family of curves y = A sinx + B cosx is ______.

Form the differential equation of all circles which pass through origin and whose centres lie on y-axis.