Question

The parabola \( y=4-x^{2} \) has vertex \( P \). It intersects \( x \)-axis at \( A \) and \( B \). If the parabola is translated from its initial position to a new position by moving its vertex along the line \( y=x+4 \), so that it intersects \( x \)-axis at \( B \) and \( C \), then abscissa of \( C \) will be : 

(a) 3 

(b) 4 

(c) 6 

(d) 8

Answer 1

y = 4- x² intersects x- axis at A and B

∵ 4 - x² = 0 gives x = -2 or 2

Hence, (-2 ,0) & (2 ,0) are coordinates of A& B

Replace x by x + y in equation (i), we get 

y = 4- (x+ 4)²

⇒ 4 - (4 + 4)²  = 0 gives intersection points with x- axis

⇒ (x+4)²  4 = (+/- 2)² 

⇒ x + 4 = -2 or x+4 = 2

⇒ x = -6 or x = -2

Hence, (-2,0)  & (-6,0) are coordinates of B & C

∴ B = (-20) , A (2,0)  C & (-6,0)

∴ abscissa of c will be -6