Determine the area enclosed by the curve $x^{2} - 10 x + 4 y + y^{2} = 196$

15 π

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

225 π

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

20 π

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

17 π

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

Open in App

Solution

The correct option is B $225 π$
Equation of the circle is
$x^{2} - 10 x + 4 y + y^{2} = 196$
$=> x^{2} - 2 \times x \times 5 + 5^{2} + y^{2} + 2 \times y \times 2 + 2^{2} = 196 + 2^{2} + 5^{2}$
$=> (x - 5)^{2} + (y + 2)^{2} = 196 + 4 + 25$
$=> (x - 5)^{2} + (y + 2)^{2} = 225$
$=> (x - 5)^{2} + (y + 2)^{2} = 15^{2}$
Thus radius of the circle is 15
Thus, area of the circle $= π \times 15^{2}$
$= 225 π$

Suggest Corrections

Similar questions

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1

y^{2} + x^{4} = x^{2}

y^{2} = x + 1

y^{2} = - x + 1

The area of the smaller portion enclosed by the curves $x^{2} + y^{2} = 9$ and $y^{2} = 8 x$ is

| y | = 1 - x^{2}

x^{2} + y^{2} = 1

Join BYJU'S Learning Program