The equation 2y^2 + 3y – 4x – 3 = 0 represents a parabola for which

Q: The equation 2y2 + 3y – 4x – 3 = 0 represents a parabola for which

(A) length of latus rectum is 4

(B) equation of the axis is 4y + 3 = 0

(C) equation of directrix is 2x + 1 = 0

(D) equation of tangent at vertex is x = -33/32

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Ans: (B) & (D)
Sol: The given equation can be re-written as $\large (y+\frac{3}{4})^2 = 2(x+\frac{33}{32})$

which is of the form Y2 = 4aX.

Hence the vertex is $ (-\frac{33}{32} , -\frac{3}{4})$

The axis is y + 3/4 = 0

⇒ y = -3/4

The directrix is x + a = 0

⇒ x +33/32 +1/2 = 0

⇒ x = -49/32

The tangent at the vertex is x + 33/32 = 0

⇒ x = -33/32

Length of the latus rectum = 4a = 2.

Hence (B) and (D) are the correct answers.