Parabola Test

Result

Parabola Test - 3

Score
-
out of -
Rank
-
out of -

TIME Taken - -

SHARING IS CARING

If our Website helped you a little, then kindly spread our voice using Social Networks. Spread our word to your readers, friends, teachers, students & all those close ones who deserve to know what you know now.

Weekly Quiz Competition

Question 1
1 / -0

From the focus of the parabola y² = 8x, tangents are drawn to the circle (x - 6)² + y² = 4. Then the equation of circle through the focus and points of contact of the tangent is

A
x² + y² + 6x – 12 = 0

B
x² + y² - 8x + 12 = 0

C
x² + y² - 6x + 12 = 0

D
x² + y² + 8x – 12 = 0

Solution

Focus of the parabola is (2, 0)
Centre of the given circle is C (6, 0)
Now, circle through S, P and Q will also pass through C.
⇒ Required circle is (x - 2) (x - 6) + y² = 0
⇒ x² + y² - 8x + 12 = 0.
Question 2
1 / -0

Statement- 1 : The locus of the centre of circle which cuts orthogonally the parabola y² = 4x at the point P (1, 2) is a circle.

Statement-2 :The tangent at P to circle is a normal to the parabola at P.

A
Both Statements-1 and Statement-2 are true and Statement-2 is the correct explanation of Statement-1

B
Both Statements-1 and Statement-2 are true and Statement-2 is not the correct explanation of Statement-1

C
Statement-1 is true and Statement-2 is false

D
Statement-1 is false and Statement-2 is true

Solution

The tangents at P to parabola is y.2 = 2 (x + 1) ⇒ y = x + 1.
It must pass through the centre of the circle so the line y = x + 1 is the desired locus.