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Published on: 13/05/2022
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Questions + Answers key
Take MCQ Maths Test1.
Find centre and radius of the following circles.
2x2+2y2−6x+4y+2 = 0
2.
Find centre and radius of the following circles.
x2 + y2+ 6x − 4y + 4 = 0
3.
Identify the type of the conic for the following equations :
11x2−25y2−44x+50y−256 = 0
4.
Identify the type of the conic for the following equations:
3x2+2y2 = 14
5.
Identify the type of conic section for each of the equations.
3x2+3y2−4x+3y+10 = 0
1.
Equation of the circle is
2x2 + 2y2 - 6x + 4y + 2 = 0
Dividing by 2, we get
x2 + y2 - 3x + 2y + 1 = 0
Here 2g = -3 ⇒ g = \(\frac { -3 }{ 2 } \)
2f = 2 ⇒ f = 1
and c = 1
∴ Centre is (-g, -f) = \(\left( \frac { 3 }{ 2 } ,-1 \right) \)
and r = \(\sqrt { { g }^{ 2 }+{ f }^{ 2 }-c } \) = \(\sqrt { { \left( \frac { 3 }{ 2 } \right) }^{ 2 }+{ 1 }^{ 2 }-1 } \)
= \(\sqrt { \frac { 9 }{ 4 } } =\frac { 3 }{ 2 } \) units.
2.
Equation of the circle is
x2 + y2 + 6x - 4y + 4 = 0.
Here 2g = 6 ⇒ g = 3
2f = -4 ⇒ f = -2 and c = 4
Centre is (-g, -f) ⇒ (-3, 2)
r = \(\sqrt { { g }^{ 2 }+{ f }^{ 2 }-c } \) = \(\sqrt { { 3 }^{ 2 }+(-2){ }^{ 2 }-{ 4 } } \)
= \(\sqrt { 9+4-4 } \)
= \(\sqrt { 9 } \)
= 3 unit
3.
A = 11, C = -25, D = -44, E = - 50, and F = -256
Here A ≠ C and A and C are of opposite signs. Hence, the given equation represents a hyperbola.
4.
Here A = 3, C = 2 and F = -14
A ≠ C and A and C are of the same sign.
Hence, the given equation represents an ellipse.
5.
Here A = 3, B = 0, C = 3, D = -4, E = 3 and F = 10
A = C and B = 0 (No xy term)
Hence, the given equations represents a circle.
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