Position of a Line with Respect to Circle

Q.

What is the condition for the line y = mx + c to be a secant of the circle $x^2+y^2=a^2$

1. 

2. 

3. 

4. 

Q. If the lines $3x-4y+4=0$ and $6x-8y-7=0$ are tangents to a circle of radius $r$, then the value of $4r$ is

Q.

Find the value of k if x + y + 5 = 0 is a tangent to the circle $x^2+y^2+10x+2ky+10=0$

1. 

2. 

3. 

4. None of these

Q.

If the lines $a_{1}x+b_{1}y+c_1=0\text{and}{a}_{2}x+b_{2}y+c_2=0$ cut the coordinates axes in concyclic points, then

1. $a_1{b}_1=a_2{b}_2$
   

2. $\frac{a_1}{a_2}=\frac{b_1}{b_2}$
   

3. $a_1+a_2=b_1+b_2$
   

4. $a_1{a}_2=b_1{b}_2$

Q. The line $y=mx$ intersects the circle $x^2+y^2-4x-4y=0$ and $x^2+y^2+6x-8y=0$ at points $A$ & $B$ (points being other than the origin). The range of $m$ such that the origin divides $AB$ internally is

1. $m>\frac{4}{3}$ or $m<-2$
2. $m>-1$
3. $-2<m<\frac{4}{3}$
4. $-1<m<\frac{3}{4}$

Q. The line $x-2y-1=0$ intersects the circle $x^2+y^2+4x-2y-5=0$ at the points $P$ and $Q$, then $\sqrt{5}PQ$ is

Q. If the line $x\cos \alpha +y\sin \alpha =p$ intersects the circle $x^2+y^2=4$ at $A$ and $B$ and chord $AB$ makes an angle of ${30}^{\circ }$ at a point on the circumference of circle then $3p^2=$

Q. If circle $x^2+y^2-6x-10y+c=0$ does not touch (or) intersect the coordinates axes and the point $(1,4)$ is inside the circle, then the range of $c$ is

1. $(6,29)$
2. $(6,25)$
3. $R-(6,25)$
4. $(25,29)$

Q. Equation of the circle, centred at $(1,–5)$ and touching the line $3x+4y=8,$ is

1. $x^2+y^2-2x+10y+1=0$
2. $x^2+y^2-4x+5y+25=0$
3. $x^2+y^2+2x-10y+26=0$
4. $x^2+y^2-10x+2y+1=0$

Q. The circle $x^2+y^2-4x-4y+4=0$ is inscribed in a triangle which has two of its sides along the coordinate axes. If the locus of the circumcenter of the triangle is $x+y-xy+k\sqrt{x^2+y^2}=0$, then the value of $k$ is

1. $2$
2. $1$
3. $3$
4. $-2$