Give an equation of a circle with center (-2,-3) ant the circle is tangent to the line y = -3/4x+ 7/4?

Question

why do they give you the line the circle is tangent to ?
What are the steps that should be followed in order to solve the problem?

Answer 1

Do this:

Draw the line with the Y intercept and the slope, then plot the center.

Once you do this, you'll find out, the radius of the circle is represented a line that passes the center and intersects the line perpendicularly. What's the formula for perpendicular line and how do you get it from the slope? (hint... slope is y over x... )

Now, you have two lines. How do you figure out a point where both intersects? (hint - both x and y are the same)

Now once you have center and the intersection, how do you figure out the distance? What's distance in this graph? Radius of the circle, right?

Now rest is just plugging in the numbers into the circle formula.

Answer 2

supply an equation of a circle with middle (-2,-3) and the circle is tangent to the line y = -3/4x + 7/4 the final equation for a circle with middle at (h,ok) is (x-h)^2 + (y-ok)^2 = r^2 the position r is the radius. So, we've (x+2)^2 + (y+3)^2 = r^2 Now we opt to locate r. The y= -3/4x +7/4 is to be tangent to the circle. for this reason the radius will be perpendicular to the line on the point of tangency. So the equation of the radius must be y= 4/3x + b. to locate b we use the coordinates of the middle of the circle to get -3= 4/3(-2) =b. This supply b= -3 +8/3 = -a million/3 S o equation of radius is y =4/3x-a million/3 at the same time as the tangent and the radius intersect we've 4/3x-a million/3 = -3/4x +7/4 4/3x +3/4x = 7/4 + a million/3 16/12x + 9/12 x. = 21/12 + 4/12 25/12 x = 25/12 x = a million y= -3/4(a million) + 7/4 = a million So the point of tangency is (a million,a million) The radius the is the gap from the middle of the circle to the point of tangency = sqrt((-2-a million)^2 + (-3-a million)^2) r = sqrt (9 +16) = sqrt (25) = 5 So, finally the equation of the circle is (x+2)^2 + (y+3)^2 = 25

Answer 3

i thins it's to calculate the radius of the circled but i 'm not quite sure