MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 5 - Circle and Conics>Competitive Thinking>Q 141

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Let the eccentricity of the hyperbola $\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1$ be reciprocal to that of the ellipse $x^{2} + 9 y^{2} = 9$ , then the ratio $a^{2} : b^{2}$ equals

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Important Questions on Circle and Conics

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MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 5 - Circle and Conics>Competitive Thinking>Q 142

Let the eccentricity of the hyperbola

\frac{x^{2}}{a^{2}} - \frac{y^{2}}{b^{2}} = 1

be the reciprocal to that of the ellipse

x^{2} + 4 y^{2} = 4

. If the hyperbola passes through a focus of the ellipse, then the focus of the hyperbola is at

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MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 5 - Circle and Conics>Competitive Thinking>Q 143

The length of the straight line

x - 3 y = 1

intercepted by the hyperbola

x^{2} - 4 y^{2} = 1

is

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MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 5 - Circle and Conics>Competitive Thinking>Q 144

The locus of the midpoints of the chords of the circle

x^{2} + y^{2} + 2 x - 2 y - 2 = 0

which make an angle of

90 °

at the centre is

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MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 5 - Circle and Conics>Competitive Thinking>Q 145

If

x + y + k = 0

touches the circle

x^{2} + y^{2} - 2 x - 4 y + 3 = 0

, then

k

can be

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MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 5 - Circle and Conics>Competitive Thinking>Q 146

If the lines

3 x - 4 y + 4 = 0

and

6 x - 8 y - 7 = 0

are tangents to a circle, then the radius of the circle is

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MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 5 - Circle and Conics>Competitive Thinking>Q 147

A chord

A B

is drawn from the point

A (0, 3)

on the circle

x^{2} + 4 x + {(y - 3)}^{2} = 0

and is extended to

M

such that

A M = 2 A B

. The locus of

M

is

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MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 5 - Circle and Conics>Competitive Thinking>Q 148

For any

a \in R

, the locus

x^{2} + y^{2} - 2 a x - 2 a y + a^{2} = 0

touches the line

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MHT-CET TRIUMPH Mathematics Multiple Choice Questions Part - 1 Based on Std. XI & XII Syllabus of MHT-CET>Chapter 5 - Circle and Conics>Competitive Thinking>Q 149

The equation of the diameter of the circle

x^{2} + y^{2} - 6 x + 2 y = 0

passing through origin is