List of top Mathematics Questions on Parabola asked in MET

The coordinates of the point on the parabola \(y = x^2 + 7x + 2\), which is nearest to the straight line \(y = 3x - 3\), are

The area of the region bounded by the parabola \((y-2)^2 = x-1\), the tangent to the parabola at the point \((2,3)\) and the X-axis, is

Solution of the differential equation \(x = 1 + xy\frac{dy}{dx} + \frac{(xy)^2}{2!}\left(\frac{dy}{dx}\right)^2 + \frac{(xy)^3}{3!}\left(\frac{dy}{dx}\right)^3 + ..........\) is

If the normal to the parabola $y²=4ax$ at the point $(at², 2at)$ cuts the parabola again at $(aT², 2aT)$, then