Solution Found!
Parabola-hyperbola tangency Let P be the parabola y = px2
Chapter 8, Problem 52RE(choose chapter or problem)
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