The centre and radius of the circle are respectively

The centre of the circle is

The equation of the circle with centre at , which passes through the point is

The foot of the perpendicular from on the line is

The foot of the perpendicular from the pole on the line is

The equation of the line parallel to and passing through is

The line passing through the points , (3,0) is

So here we used the concept of the equation of the line passing through two points. Here we also used the trigonometric terms to find the answer using the formulas. So the final solution is .

Statement-I : If  then A=
Statement-II : If  then 

Which of the above statements is true

If b > a , then the equation, (x - a) (x - b) - 1 = 0, has:

Here we used the concept of quadratic equations and solved the problem. We also understood the concept of discriminant and used it in the solution to find the intervals. Therefore, one of the roots will be in the interval of $\left(-\alpha ,a\right)$ and the other root will be in the interval $\left(b,\alpha \right)$.

If  be that roots  where ,  such that  and  then the number of integral solutions of λ is

Here we used the concept of quadratic equations and solved the problem. We also understood the concept of discriminant and used it in the solution to find the intervals. Therefore, the number of integral solutions of λ is in between 

If α,β then the equation with roots will be

Here we used the concept of quadratic equations and solved the problem. We found the sum and product of the roots first and then proceeded for the final answer. Therefore,  will be the equation for the roots  .

The equation of the directrix of the conic is

The conic with length of latus rectum 6 and eccentricity is

For the circle centre and radius are

The polar equation of the circle of radius 5 and touching the initial line at the pole is

The circle with centre at and radius 2 is