Consider the ellipse ( x^ 2 25 + y^ 2 4 =1 )

MATHEMATICS · Subjective · AP · AP Precalculus · Functions with Parameters, Vectors, and Matrices · Functions with Parameters, Vectors, and Matrices

Problem

Consider the ellipse

\dfrac{x^{2}}{25}+\dfrac{y^{2}}{4}=1

. Let

P(k,3)

be a point whose

y

-coordinate is fixed at 3 while

k

is a real parameter. (i) Find the range of values of

k

for which the point

P(k,3)

lies inside the ellipse. (ii) Determine the exact value(s) of

k

for which the point

P(k,3)

lies on the ellipse. (iii) Hence obtain the range of

k

for which the point

P(k,3)

lies outside the ellipse.