List of top Mathematics Questions on Parabola asked in UPSEE

A chord of the parabola $y = x^2 - 2x + 5$ joins the point with the abscissas $x_1 =1, x_2 = 3$ Then the equation of the tangent to the parabola parallel to the chord is :

A normal is drawn at a point $(x_1, y_1)$ of the parabola $y^2 = 16x$ and this normal makes equal angle with both $x$ and $y$ axes. Then point $(x_1, y_1)$ is