Question # 1

If (x₁, y₁) and (x₂,y₂) are the end points of a diameter then the centre of the circle is

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A square is inscribed in the circle x²+ y²- 2x + 4y + 3 =0. Its sides are parallel to the co-ordinate axes. Then one vertex of the square is

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If (0, 0) and (1, 0) are the end points of a diameter, then the equation of the circle is

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The equation of the circle with centre origin and radius r is

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x²+ y²= 1

x²+ y²= r²

x²+ y²= 0

x²- y²= r²

For the parabola the line through focus and perpendicular to the directrix is called

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Tangent

Vertex

Axis

None

The tangents drawn from the point P to a circle are real and distinct if

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P is on the circle

P is inside the circle

P is outside the circle

none of these

The second degree equation 2x2 -xy+ 5x -2y +2 =0 represents

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Circle

Hyperbola

Ellipse

Pair of straight lines

The equation of the circle wit (-1, 1) and radius 2 is

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An ellipse slides between two lines at right angles to one another. The locus of its centre is :

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a parabola

an ellipse

a circle

a hyperbola

The equation of the circle with centre (5, -2) and radius 4 is

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(x-5)²+ (y+2)²= 16

(x-5)²+ (y+2)²= 4

(x-5)²+ (y-2)²= 16

(x-5)²+ (y-2)²= 4

The tangents drawn from the point P to a circle are real and coincident if

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P is on the circle

P is inside the circle

P is outside the circle

none of these

The perpendicular bisector of any chord of a circle

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Passes through the centre of the circle

Does not pass through the centre of the circle

May or may not pass through the centre of the circle

None of these

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none of these

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1

5

7

9

A circle is a limiting case of an ellipse whose eccentricity

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Tends to a

Tends to b

Tends to 0

Tends to a + b

x =r cosθ,y= sinθ are the parametric equations of

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Circle

Ellipse

Parabola

Hyoerbola

The equation of the tangent at vertex to the parabola is y2 = -8(x -3)

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y=0

x=3

x=1

x=5

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If a plane passes through the vertex of a cone then the intersection is

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an ellipse

a hyperbola

a point circle

a parabola

The point on y²= 4ax nearest to the focus has its abciassae equal to

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-a

a

a/2

0

The tangent to the parabola y2 =4ax and perpendicular line from the focus on it meet

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x =0

y =0

x =-9

y = -a

If 2x +y + λ =0 is normal to parabola y2 =-8x,λ= _____

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12

8

24

-24

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ECAT Pre General Science Mathematics Chapter 23 Conic Section Online Test MCQs With Answers

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