The distance between the vertex of the parabola y = x2 - 4x + 3 and the centre of the circle x2 = 9 - ( y - 3 )2 is

Question

The distance between the vertex of the parabola y = x2 - 4x + 3 and the centre of the circle x2 = 9 - ( y - 3 )2 is (A) 2√3 (B) 3√2 (C) 2√2 (D) 2√5

Tardigrade Admin · Accepted Answer

Here, y = x2 - 4x + 3 ⇒ y + 1 = x2 -4x + 4 ⇒ y+ 1 = (x -2 )2 So, the vertex is (2 ,-1 ) And for the circle, x2 + (y - 3)2 = 9, the centre is (0, 3) ∴ Distance between vertex and centre =√22+(-4)2 =2√5

Q. The distance between the vertex of the parabola $y = x^{2} - 4 x + 3$ and the centre of the circle $x^{2} = 9 - (y - 3)^{2}$ is

$23$

$32$

$22$

$25$

Here, $y = x^{2} - 4 x + 3$
$\Rightarrow y + 1 = x^{2} - 4 x + 4$
$\Rightarrow y + 1 = (x - 2)^{2}$
So, the vertex is $(2, - 1)$
And for the circle, $x^{2} + (y - 3)^{2} = 9$ , the centre is $(0, 3)$
$∴$ Distance between vertex and centre
$= 2^{2} + (- 4)^{2}$
$= 25$

Q. The distance between the vertex of the parabola y=x2−4x+3 and the centre of the circle x2=9−(y−3)2 is

23​

32​

22​

25​