Answered

Westonci.ca is the ultimate Q&A platform, offering detailed and reliable answers from a knowledgeable community. Discover reliable solutions to your questions from a wide network of experts on our comprehensive Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.

Which conic section does the equation below describe?
x^2+y^2- 8x+ 10y+15 = 0
O A. Hyperbola
O B. Parabola
OC. Circle
OD. Elipse

Which Conic Section Does The Equation Below Describe X2y2 8x 10y15 0 O A Hyperbola O B Parabola OC Circle OD Elipse class=

Sagot :

Answer:

[tex]\large\boxed{\boxed{\pink {\bf \leadsto The \ equation \ represents \ a \ circle. }}}[/tex]

Step-by-step explanation:

Given equation to us is ,

[tex]\green{\implies x^2 + y^2 - 8x + 10y + 15 = 0 }[/tex]

And we need to find which conic section does the equation below describe . So for that let's simpify the Equation .

[tex]\implies x^2 + y^2 - 8x + 10y + 15 = 0 \\\\\implies x^2 - 8x + y^2 + 10y = (-15) \\\\ \implies x^2 -8x + 4^2 - 4^2 + y^2 + 10y + 5^2-5^2 + 15 = 0\\\\ \implies (x -4)^2 + (y+5)^2 - 16 - 25 + 15 = 0 \\\\ \implies (x -4)^2 + (y+5)^2 - 26 = 0 \\\\\implies (x-4)^2 + (y+5)^2 = 26 \\\\\implies (x-4)^2+(y+5)^2=(\sqrt26)^2 [/tex]

And this is similar to the standard equation for a circle is ( x - h )² + ( y - k )²= r² , where ( h, k ) is the center and r is the radius.

Hence the given equation represents a circle with center ( 4 , -5) and radius √26 units.

View image Аноним
We hope you found what you were looking for. Feel free to revisit us for more answers and updated information. Thanks for using our platform. We aim to provide accurate and up-to-date answers to all your queries. Come back soon. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.