The equation of a circle is operatorname{Re}( | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given the equation of the circle: $\operatorname{Re}(z^{2})+2(\operatorname{Im}(z))^{2}+2 \operatorname{Re}(z)=0$.Since $z=x+iy$,we have $z^{2}=x^

Vedclass · Accepted Answer

$1$

Vedclass · Answer

(A) Given the equation of the circle: $\operatorname{Re}(z^{2})+2(\operatorname{Im}(z))^{2}+2 \operatorname{Re}(z)=0$.Since $z=x+iy$,we have $z^{2}=x^{2}-y^{2}+2ixy$,so $\operatorname{Re}(z^{2})=x^{2}-y^{2}$ and $\operatorname{Im}(z)=y$.The equation becomes $(x^{2}-y^{2})+2y^{2}+2x=0$,which simplifies to $x^{2}+y^{2}+2x=0$.The center of this circle is $(-1, 0)$.Given the parabola: $x^{2}-6x-y+13=0$.Rewriting as $(x-3)^{2}-9-y+13=0$,we get $(x-3)^{2}=y-4$.The vertex of the parabola is $(3, 4)$.The line passes through $(-1, 0)$ and $(3, 4)$.The slope $m = \frac{4-0}{3-(-1)} = \frac{4}{4} = 1$.The equation of the line is $y-0=1(x+1)$,which is $y=x+1$.The $y$-intercept is the value of $y$ when $x=0$,which is $1$.

The equation of a circle is $\operatorname{Re}(z^{2})+2(\operatorname{Im}(z))^{2}+2 \operatorname{Re}(z)=0$,where $z=x+iy$. $A$ line which passes through the center of the given circle and the vertex of the parabola $x^{2}-6x-y+13=0$ has a $y$-intercept equal to $.....$

Similar Questions

$A$ circle is concentric with the circle $x^2 + y^2 - 6x + 12y + 15 = 0$ and has an area double that of the given circle. The equation of the circle is:

$A(2,3)$ and $B(-1,1)$ are two points. If $P(x,y)$ is a variable point such that $\angle APB = 90^{\circ}$,then the locus of $P$ is:

Let the circle $S$ which is concentric with the circle $x^2+y^2-2x+ky+4=0$ pass through the point $(3,-2)$. If one of the diameters of $S$ lies along the line $3x-2y+4=0$,then the radius of the circle $S$ is

Find the centre and radius of the circle $x^{2}+y^{2}-8x+10y-12=0$.

Find the equation of the circle which passes through the origin and cuts off intercepts of $-2$ and $3$ on the $x$ and $y$ axes,respectively.

Vedclass Test Series

Exam Paper Generator

Online Exam Module