Friday

December 19, 2014

December 19, 2014

Posted by **Stan** on Sunday, May 29, 2011 at 12:46am.

- Math -
**MathMate**, Sunday, May 29, 2011 at 8:19amThe roots of the parabola are known (-3 and 6), so the equation of the parabola is in the form:

k(x+3)(x-6)=0 or

k(x²-3x-18)=0 ...(1)

where k is a constant to be determined.

Since the y-intercept is negative, k>0.

If ∠ABC is a right angle, then a circle with AB as diameter intersects the y-axis at intercepts (0,p) and (0,-p) where p<0.

The centre of circle ABC is at ((6-3)/2,0), or (1.5,0), and the radius is (6-(-3))/2 = 4.5.

The equation of circle ABC is therefore:

C1 : (x-1.5)^2+y^2=4.5^2, or

C1: (x-1.5)^2 + y^2 = 20.25

To find intersection with the y-axis, substitute x=0 in C1 and solve for y to get

y=±√18=±3√2

So p=-3√2.

The constant term of equation (1) should equal p (both are y-intercepts), which leads to:

-3√2 = -18k

Solve for k and substitute in (1) to get the equation of the parabola, and hence calculate (abc)^2 as required.

**Answer this Question**

**Related Questions**

precalculus - graph the parabola y=2x^2-6x-3. plot point on the parabola A[1,-7...

Parabola Help - by plotting the graph of parabola y=2+3x-2x^2 which 3 option are...

math - A parabola has the equation y = 4(x-3)^2-7 Choose 2 true statements: A) ...

math - A parabola has the equation y = 4(x-3)^2-7 Choose 2 true statements: A) ...

Calculus - Find expressions for the quadratic functions whose graphs are shown. ...

Calculus - find the parabola whose minimum is at (7,6) rather than the point ...

Algebra: Parabolas - I have a math problem that requires me to find the focal ...

Alg II/Trig - A parabola has a vertex at (0,0); a horizontal axis; and the point...

pre cal - What is the center of the conic whose equation is x^2 + 2y^2 - 6x + ...

geometry - obtuse triangle ABC with obtuse angle B. Point D on side AC such that...