Question # 1

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

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 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

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

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 with centre at (5, -2) and radius 4 is

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None of these

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Apollonius was a

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rocket

Muslim scientist

Greek mathematicians

method of finding conics

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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The vertex of the cone is also called

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nappes

axis

rulings

apex

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a = b , h = 0

f = g, h = 0

h = h, c = 0

The generators of a cone are also called

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rulings

apex

nappes

ellipse

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1

2

0

None of these

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 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

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

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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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Three Independent Variables

Two independent constant

Three independent parameters

Three independent constant

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

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

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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ECAT Mathematics Chapter 22 Circle Online Test MCQs With Answers

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