Find the set of value(s) for which the point P(a,-a) lies inside the ellipse $\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1$ .

Open in App

Solution

If P(a.-a) lies inside the given ellipse. $∴ S_{1} < 0 \Rightarrow \frac{a^{2}}{16} + \frac{a^{2}}{9} - 1 < 0 \Rightarrow \frac{25}{144} a^{2} < 1 \Rightarrow a^{2} < \frac{144}{25} ∴ a \in (- \frac{12}{5}, \frac{12}{5})$

Suggest Corrections

Similar questions

Q. Find the set of value(s) of

α

for which the point

(7 - \frac{5}{4} α, α)

lies inside the ellipse

\frac{x^{2}}{25} + \frac{y^{2}}{16} = 1.

Q. Find the set of those value (s) of

^{'} α^{'}

for which the point

(7 - \frac{5}{4} α, α)

lies inside the ellipse

\frac{x^{2}}{25} + \frac{y^{2}}{16} = 1

Q. Point

(1, 2)

lies _____ the ellipse

\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1

Q. The point

(4 cos θ, 4 sin θ)

lies ____________ the ellipse

\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1

Find the set of value (s) of $^{'} λ^{'}$ for which the line $3 x - 4 y + λ = 0$ intersect the ellipse $\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1$ at two distinct points.

Join BYJU'S Learning Program

Find the set of value(s) for which the point P(a,-a) lies inside the ellipse x216+y29=1 .

If P(a.-a) lies inside the given ellipse. ∴S1<0⇒a216+a29−1<0⇒25144a2<1⇒a2<14425∴a∈(−125,125)

Find the set of value(s) for which the point P(a,-a) lies inside the ellipse $\frac{x^{2}}{16} + \frac{y^{2}}{9} = 1$ .

If P(a.-a) lies inside the given ellipse. $∴ S_{1} < 0 \Rightarrow \frac{a^{2}}{16} + \frac{a^{2}}{9} - 1 < 0 \Rightarrow \frac{25}{144} a^{2} < 1 \Rightarrow a^{2} < \frac{144}{25} ∴ a \in (- \frac{12}{5}, \frac{12}{5})$