Find the condition for the line x cos - - y sin - - P to be a tangent to the ellipse x2-a2 - y2-b2 - 1-

The correct option is A P^2 = a^2 cos^2 θ + b^2 sin^2 θ x cos θ + y sin θ = P y= cosθ #160; x sinθ #160; #160; + P sinθ #160; ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Sin(A+B)Sin(A-B)

Find the cond...

Question

Find the condition for the line $x cos θ + y sin θ = P$ to be a tangent to the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1.$

P^{2} = a^{2} {cos}^{2} θ + b^{2} {sin}^{2} θ

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

P^{2} = a^{2} {cos}^{2} θ - b^{2} {sin}^{2} θ

No worries! We‘ve got your back. Try BYJU‘S free classes today!

P^{2} = b^{2} {cos}^{2} θ + a^{2} {sin}^{2} θ

No worries! We‘ve got your back. Try BYJU‘S free classes today!

P^{2} = b^{2} {cos}^{2} θ - a^{2} {sin}^{2} θ

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $P^{2} = a^{2} {cos}^{2} θ + b^{2} {sin}^{2} θ$
$x cos θ + y sin θ = P$
$y = - \frac{cos θ x}{sin θ} + \frac{P}{sin θ}$
Condition of tangency is $c^{2} = a^{2} m^{2} + b^{2}$
$\Rightarrow \frac{P^{2}}{{sin}^{2} θ} = a^{2} \frac{{cos}^{2} θ}{{sin}^{2} θ} + b^{2}$
$\Rightarrow P^{2} = a^{2} {cos}^{2} θ + b^{2} {sin}^{2} θ$

Suggest Corrections

Similar questions

Q. If

μ = \sqrt{a^{2} {cos}^{2} θ + b^{2} {sin}^{2} θ} + \sqrt{a^{2} {sin}^{2} θ + b^{2} {cos}^{2} θ}

then the difference between maximum and minimum values of

μ^{2}

is:

Q. If

u = \sqrt{a^{2} {cos}^{2} θ + b^{2} {sin}^{2} θ} +

\sqrt{a^{2} {sin}^{2} θ + b^{2} {cos}^{2} θ}

, then the difference between the maximum and minimum values of

u^{2}

is given by

If $u = \sqrt{a^{2} c o s^{2} θ + b^{2} s i n^{2} θ} + \sqrt{a^{2} s i n^{2} θ + b^{2} c o s^{2} θ}$ , then the difference between the maximum and minimum values of $u^{2}$ is given by

Q. If

p^{2} = a^{2} {cos}^{2} θ + b^{2} {sin}^{2} θ

then

\frac{d^{2} p}{d θ^{2}} + p

is equal to

(a \neq b)

Q. If

p^{2} = a^{2} c o s^{2} θ + b^{2} s i n^{2} θ

then Prove That:

P + \frac{d^{2} p}{d θ^{2}} = \frac{a^{2} b^{2}}{p^{3}}

Join BYJU'S Learning Program

Find the condition for the line xcosθ+ysinθ=P to be a tangent to the ellipse x2a2+y2b2=1.

The correct option is A P2=a2cos2θ+b2sin2θxcosθ+ysinθ=Py=−cosθxsinθ+PsinθCondition of tangency is c2=a2m2+b2⇒P2sin2θ=a2cos2θsin2θ+b2⇒P2=a2cos2θ+b2sin2θ

Find the condition for the line $x cos θ + y sin θ = P$ to be a tangent to the ellipse $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1.$