Question

The equation $$2{x^2} + 3{y^2} - 8x - 18y + 35 = k$$       represents :

A. no locus if $$k>0$$
B. an ellipse if $$k<0$$
C. a point if $$k=0$$  
D. a hyperbola if $$k>0$$
Answer :   a point if $$k=0$$
Solution :
We have $$2{x^2} + 3{y^2} - 8x - 18y + 35 = k$$
$$ \Rightarrow 2{\left( {x - 2} \right)^2} + 3{\left( {y - 3} \right)^2} = k$$
For $$k=0,$$   we get $$ \Rightarrow 2{\left( {x - 2} \right)^2} + 3{\left( {y - 3} \right)^2} = 0$$      which represents the point $$\left( {2,\,3} \right).$$

Releted MCQ Question on
Geometry >> Locus

Releted Question 1

The equation $$\frac{{{x^2}}}{{1 - r}} - \frac{{{y^2}}}{{1 + r}} = 1,\,\,\,r > 1$$       represents :

A. an ellipse
B. a hyperbola
C. a circle
D. none of these
View Answer
Releted Question 2

The equation $$2{x^2} + 3{y^2} - 8x - 18y + 35 = k$$       represents :

A. no locus if $$k>0$$
B. an ellipse if $$k<0$$
C. a point if $$k=0$$
D. a hyperbola if $$k>0$$
View Answer
Releted Question 3

If $$a>2b>0$$    then the positive value of $$m$$ for which $$y = mx - b\sqrt {1 + {m^2}} $$     is a common tangent to $${x^2} + {y^2} = {b^2}$$   and $${\left( {x - a} \right)^2} + {y^2} = {b^2}$$    is :

A. $$\frac{{2b}}{{\sqrt {{a^2} - 4{b^2}} }}$$
B. $$\frac{{\sqrt {{a^2} - 4{b^2}} }}{{2b}}$$
C. $$\frac{{2b}}{{a - 2b}}$$
D. $$\frac{b}{{a - 2b}}$$
View Answer
Releted Question 4

The locus of the mid-point of the line segment joining the focus to a moving point on the parabola $${y^2} = 4ax$$   is another parabola with directrix :

A. $$x = - a$$
B. $$x = - \frac{a}{2}$$
C. $$x = 0$$
D. $$x = \frac{a}{2}$$
View Answer

Practice More Releted MCQ Question on
Locus

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AlgebraSequences and SeriesQuadratic EquationComplex NumberMatrices and DeterminantsPermutation and CombinationBinomial TheoremMathematical InductionMathematical Reasoning
Statistics and ProbabilityStatisticsProbability
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