# The cartesion equation of the curve $x=7+4\:\cos \alpha ,y=-3+4\sin \alpha\:is$ Option 1) $x^{2}+y^{2}-14x+6y+42=0$ Option 2) $x^{2}+y^{2}-6x+14y+21=0$ Option 3) $x^{2}+y^{2}-10x+12y+28=0$ Option 4) None of these

P Plabita

Locus -

Path followed by a point p(x,y) under given condition (s).

- wherein

It is satisfied by all the points (x,y) on the locus.

$Cos \alpha=\frac{x-7}{4}$

$Sin \alpha=\frac{y+3}{4}$

So $\left ( \frac{x-7}{4} \right )^{2}$+ $\left ( \frac{y+3}{4} \right )^{2}=1$

$x^{2} + y^{2} -14x+6y+42=0$

Option 1)

$x^{2}+y^{2}-14x+6y+42=0$

This is correct option

Option 2)

$x^{2}+y^{2}-6x+14y+21=0$

This is incorrect option

Option 3)

$x^{2}+y^{2}-10x+12y+28=0$

This is incorrect option

Option 4)

None of these

This is incorrect option

Exams
Articles
Questions