Goodafternoon.,pasagot naman po ng tanong na ito,.

1. Find the equation of the circle tangent to the lines

5x + 12y - 161= 0 and 12x + 5y - 126 = 0 and passing through the point (-9,-11).

Thank you so much for your response. :-)

June 25, 2016 - 4:57pm

#1
charlie_09

Equation of circle tangent to two lines and passing through a point

Goodafternoon.,pasagot naman po ng tanong na ito,.

1. Find the equation of the circle tangent to the lines

5x + 12y - 161= 0 and 12x + 5y - 126 = 0 and passing through the point (-9,-11).

Thank you so much for your response. :-)

- 1563 reads

Subscribe to MATHalino on

- Tapered Beam
- Vickers hardness: Distance between indentations
- Time rates
- Minima Maxima: y=ax³+bx²+cx+d
- Make the curve y=ax³+bx²+cx+d have a critical point at (0,-2) and also be a tangent to the line 3x+y+3=0 at (-1,0).
- Minima maxima: Arbitrary constants for a cubic
- Minima Maxima: 9a³y=x(4a-x)³
- Minima maxima: a²y = x⁴
- how to find the distance when calculating moment of force
- strength of materials
- Analytic Geometry Problem Set [Locked: Multiple Questions]
- Equation of circle tangent to two lines and passing through a point
- Product of Areas of Three Dissimilar Right Triangles
- Perimeter of Right Triangle by Tangents
- Differential equations
- Laplace
- Families of Curves: family of circles with center on the line y= -x and passing through the origin
- Family of Plane Curves
- Differential equation
- Differential equation

Home • Forums • Blogs • Glossary • Recent

About • Contact us • Disclaimer • Privacy Policy • Hosted by WebFaction • Powered by Drupal

About • Contact us • Disclaimer • Privacy Policy • Hosted by WebFaction • Powered by Drupal

Forum posts (unless otherwise specified) licensed under a Creative Commons Licence.

All trademarks and copyrights on this page are owned by their respective owners. Forum posts are owned by the individual posters.

All trademarks and copyrights on this page are owned by their respective owners. Forum posts are owned by the individual posters.

Formulas to use$d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$

Distance from a line to a point

$d = \dfrac{ax_1 + by_1 + c}{\pm \sqrt{a^2 + b^2}}$

$r_1 = \sqrt{(h + 9)^2 + (k + 11)^2}$

$r_2 = \dfrac{5h + 12k - 161}{(+)(-)\sqrt{5^2 + 12^2}} = \dfrac{5h + 12k - 161}{-13}$

$r_3 = \dfrac{12h + 5k - 126}{(+)(-)\sqrt{12^2 + 5^2}} = \dfrac{12h + 5k - 126}{-13}$

$r_2 = r_3$

$\dfrac{5h + 12k - 161}{-13} = \dfrac{12h + 5k - 126}{-13}$

$5h + 12k - 161 = 12h + 5k - 126$

$-7h + 7k - 35 = 0$

$h = k - 5$

$r_1 = r_2$

$\sqrt{(h + 9)^2 + (k + 11)^2} = \dfrac{5h + 12k - 161}{-13}$

$(h + 9)^2 + (k + 11)^2 = \dfrac{(5h + 12k - 161)^2}{169}$

$169(h + 9)^2 + 169(k + 11)^2 = (5h + 12k - 161)^2$

$169(h^2 + 18h + 81) + 169(k^2 + 22k + 121) \\ ~ ~ ~ ~ ~ = (5h)^2 + (12k)^2 + (-161)^2 + 2(5h)(12k) + 2(5h)(-161) + 2(12k)(-161)$

$(169h^2 + 3\,042h + 13\,689) + (169k^2 + 3\,718k + 20\,449) \\ ~ ~ ~ ~ ~ = 25h^2 + 144k^2 + 25\,921 + 120hk - 1\,610h - 3\,864k$

$144h^2 + 25k^2 - 120hk + 4\,652h + 7\,582k + 8\,217 = 0$

$144(k - 5)^2 + 25k^2 - 120(k - 5)k + 4\,652(k - 5) + 7\,582k + 8\,217 = 0$

$144(k^2 - 10k + 25) + 25k^2 - (120k^2 - 600k) + (4\,652k - 23\,260) + 7\,582k + 8\,217 = 0$

$144k^2 - 1\,440k + 3\,600 + 25k^2 - 120k^2 + 600k + 4\,652k - 23\,260 + 7\,582k + 8\,217 = 0$

$49k^2 + 11\,394k - 11\,443 = 0$

Now you can take it from here. Solve for k and solve for h then find the radius r. The solution is a little ugly because of the equations involved, I hope somebody will share a more beautiful approach.

Ano po ang next step?

from the above equation, k=1,then h=-4.solve for r from any equation for r above. then substitute the values in the equation of circle and transform to standard form.