Question

The centre of the conic section $$14{x^2} - 4xy + 11{y^2} - 44x - 58y + 71 = 0$$         is :

A. $$\left( {2,\,3} \right)$$  
B. $$\left( {2,\, - 3} \right)$$
C. $$\left( { - 2,\,3} \right)$$
D. $$\left( { - 2,\, - 3} \right)$$
Answer :   $$\left( {2,\,3} \right)$$
Solution :
For centre, $$\frac{{\partial S}}{{\partial x}} = 0,\,\frac{{\partial S}}{{\partial y}} = 0,\,\,\, \Rightarrow 7x - y - 11 = 0,\,\,2x - 11y + 29 = 0.$$           Solve.

Releted MCQ Question on
Geometry >> Ellipse

Releted Question 1

Let $$E$$ be the ellipse $$\frac{{{x^2}}}{9} + \frac{{{y^2}}}{4} = 1$$   and $$C$$ be the circle $${x^2} + {y^2} = 9.$$   Let $$P$$ and $$Q$$ be the points $$\left( {1,\,2} \right)$$  and $$\left( {2,\,1} \right)$$  respectively. Then-

A. $$Q$$ lies inside $$C$$ but outside $$E$$
B. $$Q$$ lies outside both $$C$$ and $$E$$
C. $$P$$ lies inside both $$C$$ and $$E$$
D. $$P$$ lies inside $$C$$ but outside $$E$$
View Answer
Releted Question 2

The radius of the circle passing through the foci of the ellipse $$\frac{{{x^2}}}{{16}} + \frac{{{y^2}}}{9} = 1,$$   and having its centre at $$\left( {0,\,3} \right)$$  is-

A. $$4$$
B. $$3$$
C. $$\sqrt {\frac{1}{2}} $$
D. $$\frac{7}{2}$$
View Answer
Releted Question 3

The area of the quadrilateral formed by the tangents at the end points of latus rectum to the ellipse $$\frac{{{x^2}}}{9} + \frac{{{y^2}}}{5} = 1,$$    is-

A. $$\frac{{27}}{4}\,\,{\text{sq}}{\text{.}}\,{\text{units}}$$
B. $$9\,\,{\text{sq}}{\text{.}}\,{\text{units}}$$
C. $$\frac{{27}}{2}\,\,{\text{sq}}{\text{.}}\,{\text{units}}$$
D. $$27\,\,{\text{sq}}{\text{.}}\,{\text{units}}$$
View Answer
Releted Question 4

If tangents are drawn to the ellipse $${x^2} + 2{y^2} = 2,$$   then the locus of the mid-point of the intercept made by the tangents between the coordinate axes is-

A. $$\frac{1}{{2{x^2}}} + \frac{1}{{4{y^2}}} = 1$$
B. $$\frac{1}{{4{x^2}}} + \frac{1}{{2{y^2}}} = 1$$
C. $$\frac{{{x^2}}}{2} + \frac{{{y^2}}}{4} = 1$$
D. $$\frac{{{x^2}}}{4} + \frac{{{y^2}}}{2} = 1$$
View Answer

Practice More Releted MCQ Question on
Ellipse

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AlgebraSequences and SeriesQuadratic EquationComplex NumberMatrices and DeterminantsPermutation and CombinationBinomial TheoremMathematical InductionMathematical Reasoning
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CalculusSets and RelationsFunctionLimitsContinuityDifferentiability and DifferentiationApplication of DerivativesDifferential EquationsIndefinite IntegrationDefinite IntegrationApplication of Integration
GeometryStraight LinesCircleParabolaEllipseHyperbolaLocus3D Geometry and VectorsThree Dimensional Geometry
TrigonometryTrigonometric Ratio and IdentitiesTrignometric EquationsProperties and Solutons of TriangleInverse Trigonometry Function