Equation of Circle with Origin as Center

Q. If the chord y = mx + 1 of the circle $x^2+y^2=1$ subtends an angle of measure ${45}^{\circ }$ at the major segment of the circle then value of m is

1. 2
2. -2
3. -1
4. none of these

Q. Consider a region $M$ which contains all the points $(x,y)$ such that $x^2+y^2\le 100$ and $\sin (x+y)\ge 0$ where $x,y\in R$. If the area of region $M$ is $m\pi$ sq units, then the value of $m$ is

Q. For how many values of p does the circle $x^2+y^2+2x+4y-p=0$ and the coordinate axes have exactly three common points?
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Q.

The equation of circle with centre $(1,1)$ and radius 4 is given by $(x-1{)}^2+(y-1{)}^2=4$

1. True

2. False

Q. Let C be the circle with centre (0, 0) and radius 3 units. The equation of the locus of the midpoints of the chords of the circle C that subtend an angle of $\frac{2\pi }{3}$ at its centre is -

1. $x^2+y^2=\frac{27}{4}$
2. $x^2+y^2=\frac{9}{4}$
3. $x^2+y^2=\frac{3}{2}$
4. $x^2+y^2=1$

Q. A straight line $L_1:\frac{x}{a}+\frac{y}{b}=1$ intersects the $x$-axis and $y$-axis at $P$ and $Q$ respectively and a straight line $L_2$ perpendicular to $L_1$ cuts the $x$-axis and $y$-axis at $R$ and $S$ respectively. The locus of the point of intersection of the lines $PS$ and $QR$ is

1. $x^2+y^2+ax-by=0$
2. $x^2+y^2-ax-by=0$
3. $x^2-y^2-ax-by=0$
4. $x^2+y^2+ax+by=0$

Q. The locus of the centre of circle which touches $(y-1{)}^2+x^2=1$ externally and also touches x-axis, is

1. $\{x^2=4y,y\ge 0\}\cup \left\{\right(0,y),y<0\}$
2. $x^2=y$
3. $y=4x^2$
4. $y^2=4x\cup (0,y),yϵR$