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A) A circle

B) An ellipse

C) A horizontal line

D) A hyperbola

E) A vertical line

Answer

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Using ${cos\theta = }\dfrac{{\text{x}}}{{\text{r}}}$ in the given polar coordinate equation,

And so on simplifying we can get ${{\text{r}}^{\text{2}}}{\text{ = 10x}}$

As we know that equation of circle is $\sqrt {{{\text{x}}^{\text{2}}}{\text{ + }}{{\text{y}}^{\text{2}}}} {\text{ = r}}$

Put the value of ${{\text{r}}^{\text{2}}}$in the equation of the circle . and so the equation will be simplified to

${{\text{x}}^{\text{2}}}{\text{ + }}{{\text{y}}^{\text{2}}}{\text{ = 10x}}$

Make the perfect square of both the variables as to convert it in the equation of circle if possible,

\[{{\text{x}}^{\text{2}}}{\text{ - 10x + }}{{\text{y}}^{\text{2}}}{\text{ + 25 - 25 = 0}}\]

\[{\left( {{\text{x - 5}}} \right)^{\text{2}}}{\text{ + }}{{\text{y}}^{\text{2}}}{\text{ = 25}}\]

So from the above equation we can state that through the above given polar coordinates if converted into Cartesian coordinates then it will be a circle.

In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction. The x and y coordinates of a point measure the respective distances from the point to a pair of perpendicular lines in the plane called the coordinate axes, which meet at the origin.