Solve for the equation in standard form of the following conic sections and graph the curve on a Cartesian plane indicating important points. 1. An el

kuCAu

kuCAu

Answered question

2020-11-10

Solve for the equation in standard form of the following conic sections and graph the curve on a Cartesian plane indicating important points.
1. An ellipse passing through (4, 3) and (6, 2)
2. A parabola with axis parallel to the x-axis and passing through (5, 4), (11, -2) and (21, -4)
3. The hyperbola given by 5x24y2=20x+24y+36.

Answer & Explanation

Ezra Herbert

Ezra Herbert

Skilled2020-11-11Added 99 answers

Step 1
An equation of the ellipse is of the form,
x2a2+y2b2=1
Equation of the ellipse through the point (4, 3).
So, x=4,y=3 satisfies the equation of an ellipse.
Implies that,
42a2+32b2=1
16a2+9b2=1
16a2=19b2
1a2=116(19b2)
Step 2
Equation of the ellipse through the point (6, 2).
So, x=6,y=2 satisfies the equation of an ellipse.
62a2+22b2=1
36a2+4b2=1
36a2=14b2
1a2=136(14b2)
Step 3
Compare equations (1) and (2), we get
136(14b2)=116(19b2)
Multiply both sides by 4,
19(14b2)=14(19b2)
Distribute both sides,
1949b2=1494b2
Combine like terms
1914=49b294b2
Make the same denominator,
436936=1636b28136b2
536=6536b2
536=6536b2
Multiply both sides by 36,
51=65b2
Divide both sides by -65,
565=1b2
By simplifying it,
113=1b2
Taking reciprocal from both sides,
b2=13
Step 4
Substitute b2=13
in the equation 1a2=116(19b2),

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?