the curve represented by x 2 cos t sin t y 5 cos t sin t is

The curve represented by $$x = 2\left( {\cos \,t + \sin \,t} \right),\,y\, = 5\left( {\cos \,t - \sin \,t} \right)$$ is :

A. a circle

B. a parabola

C. an ellipse

D. a hyperbola

Answer : an ellipse

Solution :
$$\eqalign{ & x = 2\left( {\cos \,t + \sin \,t} \right) \cr & y\, = 5\left( {\cos \,t - \sin \,t} \right) \cr & \Rightarrow \frac{{{x^2}}}{4} + \frac{{{y^2}}}{{25}} = 2 \Rightarrow {\text{Ellipes}} \cr} $$

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

The curve represented by $$x = 2\left( {\cos \,t + \sin \,t} \right),\,y\, = 5\left( {\cos \,t - \sin \,t} \right)$$ is :

Releted MCQ Question on
Geometry >> Locus

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

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

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 :

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 :

Practice More Releted MCQ Question on
Locus

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The curve represented by $$x = 2\left( {\cos \,t + \sin \,t} \right),\,y\, = 5\left( {\cos \,t - \sin \,t} \right)$$ is :

Releted MCQ Question on Geometry >> Locus

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

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

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 :

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 :

Practice More Releted MCQ Question on Locus

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Releted MCQ Question on
Geometry >> Locus

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Locus