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Parabola-hyperbola tangency Let P be the parabola y = px2

Chapter 8, Problem 52RE

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QUESTION:

Parabola-hyperbola tangency Let P be the parabola \(y=p x^{2}\) and H be the right half of the hyperbola \(x^{2}-y^{2}=1\).

a. For what value of p is P tangent to H?

b. At what point does the tangency occur?

c. Generalize your results for the hyperbola \(x^{2} / a^{2}-y^{2} / b^{2}=1\).

Questions & Answers

QUESTION:

Parabola-hyperbola tangency Let P be the parabola \(y=p x^{2}\) and H be the right half of the hyperbola \(x^{2}-y^{2}=1\).

a. For what value of p is P tangent to H?

b. At what point does the tangency occur?

c. Generalize your results for the hyperbola \(x^{2} / a^{2}-y^{2} / b^{2}=1\).

ANSWER:

Solution 52RE

Step 1:

Let P be the parabola and H be the right half of the hyperbola .

To find: a. For what value of p is P tangent to H?

Given

Given

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