Equation of Family of Circles Touching a Line and Passing through a Given Point on the Line

Q.

The locus of the point p(x, y) satisfying the relation $\sqrt{(x-3{)}^2+(y-1{)}^2}+\sqrt{(x+3{)}^2+(y-1{)}^2}=6$ is

1. Line segment

2. Circle

3. Ellipse

4. Straight line

Q. 29. Find the area of the triangle formed by the straight lines whoes equations x+2y-5=0, 2x+y-7=0 and x-y+1=0 without determining the coordinates of the vertices of the triangle.also compute the tangent of the interior angles of the triangle and hence comment upon the nature of triangle.

Q. 23. find equation of circle touching the line x+y=2 at (1, 1) and having radius root2 unit?

Q. find the equation of circle touching 3x-4y+1=0 at (1, 1) and having radius 10 uni

Q.

The circle passing through the point (-1, 0) and touching the y-axis at (0, 2) also passes through the point.

1. 

2. 

3. 

4. (-4, 0)

Q.

Statement 1: If a line $L=0$ is tangent to the circle $S=0$, then it will also be a tangent to the circle $S+\lambda L=0$

Statement 2: If a line touches a circle, then perpendicular distance of the line from the centre of the circle is equal to the radius of the circle.

1. Statement 1 is true, statement 2 is true, statement 2 is correct explanation for statement 1

2. Statement 1 is true, Statement 2 is true, statement 2 is NOT a correct explanation for statement 1

3. Statement 1 is true, Statement 2 is false

4. Statement 1 is false, statement 2 is true

Q.

Statement 1: If a line $L=0$ is tangent to the circle $S=0$, then it will also be a tangent to the circle $S+\lambda L=0$

Statement 2: If a line touches a circle, then perpendicular distance of the line from the centre of the circle is equal to the radius of the circle.

1. Statement 1 is true, statement 2 is true, statement 2 is correct explanation for statement 1

2. Statement 1 is true, Statement 2 is true, statement 2 is NOT a correct explanation for statement 1

3. Statement 1 is true, Statement 2 is false

4. Statement 1 is false, statement 2 is true

Q. Consider a family of circles which are passing through the point (–1, 1) and has x-axis as its tangents. If (h, k) are the co-ordinates of the centre of the circles, then the set of values of k is given by the interval

1. 0 $<$ k $<$ $\frac{1}{2}$
2. k $\ge$ $\frac{1}{2}$
3. $-\frac{1}{2}$$\le$ k $\le$ $\frac{1}{2}$
4. k $\le$ $\frac{1}{2}$

Q. If a circle S(x, y)=0 touches the line x + y = 5 at the point (2, 3) and S(1, 2) = 0, then the radius of such circle is .

1. $r=\frac{3}{2}\mathrm{units}$
2. $r=\frac{1}{2}\mathrm{units}$
3. $r=\frac{3}{\sqrt{2}}\mathrm{units}$
4. $r=\frac{1}{\sqrt{2}}\mathrm{units}$