# The line 3x-2y+k=0, where k is a constant, intersects the curve x^2 + y^2 -4x-9=0 at two points. Find the range of k?

##### 1 Answer

#### Answer:

Range of

#### Explanation:

To find points of intersection of a line and curve, we should solve them as simultaneous equation.

Here we have a linear equation indicating a line and a quadratc equation indicating a conic section (actually a circle). When we substitute one variable in terms of another variable from linear equation in to quadratic equation, we get a quadratic equation in other variable.

If the quadratic equation has two roots, they intersect at two points and if it has one root, it is a tangent. In case it has no roots, it means line does not intersect the conic section at all.

Here we have

or

or

or

It will have two roots if discriminant is greater than zero i.e.

or

or

or

or

This is so, when **either**

**or**

Hence solution is