Parabola and Ellipse — NDA Mathematics PYQs

A tangent to the parabola $y^2=4x$ is inclined at an angle $45°$ with the positive direction of $x$-axis. What is the point of contact of the tangent and the parabola?

If any point on an ellipse is $(3\sin \alpha ,5\cos \alpha )$, then what is the eccentricity of the ellipse?

Consider the following statements in respect of the equation $x^2+3y=0$ :
I. The equation represents the equation to parabola that opens upwards.
II. The axis of the parabola is $x=0$.
III. The equation of the latus rectum is $4y-3=0$.
How many of the statements given above are correct?