Question # 1

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

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The vertex of the cone is also called

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nappes

axis

rulings

apex

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None of these

Apollonius was a

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rocket

Muslim scientist

Greek mathematicians

method of finding conics

The equation: x²+ y²+ 2gx + 2fy + c = 0, represents

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pair of lines

a circle

a general second degree equation

a hyperbola

IF the cone is cut by a plane perpendicular to the axis of the cone, then the section is a

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circle

ellipse

hyperbola

parabola

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A second degree equation in which coefficients of x²and y²are equal and there is no product term xy represents

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a parabola

a circle

an ellipse

a pair of lines

The area of the circle centred at (1, 2) and passing through (4, 6) is

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If the intersecting plane is parallel to a generator of the cone, but intersects its one nappe only, the curve of intersection is

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a circle

an ellipse

a parabola

a hyperbola

If the cutting plane is parallel to the axis of the cone and intersects both of its nappes, then the curve of intersection is

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an ellipse

a circle

a parabola

a hyperbola

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

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an ellipse

a parabola

a hyperbola

a point circle

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1

2

0

None of these

The generators of a cone are also called

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rulings

apex

nappes

ellipse

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If the cutting plane is slightly tilted and cuts only one nappe of the cone, the resulting section is

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an ellipse

a circle

a hyperbola

a parabola

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To study conics, Pappus used the method of

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analytic geometry

solid geometry

Euclidean geometry

none of these

A cone is generated by all lines through a fixed point and the circumference of

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a circle

an ellipse

a hyperbola

none of these

The set of all points in the plane that are equally distant from a fixed point is called a

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parabola

ellipse

hyperbola

circle

The equation of the circle whose centre is (-3, 5) and having radius 7 is

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(x-3)²+ (y+5)²= 7²

(x-3)²+ (y-5)²= 7²

x²+y²+6x-10y-15=0

The fixed point which lies on the axis of the cone is called its

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axis

apex

nappes

axis

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If three non-collinear points through which a circle passes are known, then we can find the

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variables x and y

value of x and c

three constant f, g and c

inverse of the circle

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Three Independent Variables

Two independent constant

Three independent parameters

Three independent constant

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a = b , h = 0

f = g, h = 0

h = h, c = 0

If the cutting plane is parallel to the axis of the cone and intersects both of its nappes, then the curve of intersection is

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an ellipse

a circle

a parabola

a hyperbola

If the centre of the circle is the origin, then equation of the cirlce is

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x²+ y²= 0

2gx + 2fy - c = 0

x²+ y²= r²

gx + fy - c/2 = 0

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Mathematics ECAT Pre Engineering Chapter 22 Circle Online Test MCQs With Answers

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