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Kelompok 6

It's talk about The Equation of the Target Line on a Circle

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Kelompok 6

1. 1. The Equation of the Target Line on a Circle Group 6 Audi Renata Fajri Parmi Junia Handayanis LupitaYessica
2. 2. <ul><li>Equation of the Tangent Line on a circle through point of T (x,y) </li></ul><ul><li>With center of (0,0) </li></ul><ul><li>Gradient TO, m TO = </li></ul><ul><li>Gradient h, m h = - </li></ul>O T(x,y) h
3. 3. <ul><li>So, </li></ul><ul><li>Because point T(x 1 ,y 1 ) is located inside the circle x 2 +y 2 =r 2 .....(2) substitute equation (1) and (2) </li></ul>
4. 4. <ul><li>With center of P (a,b) </li></ul>P(a,b) r T(x,y) x y 0
5. 5. <ul><li>Gradient line of TP is m TP = </li></ul><ul><li>Tangent line of h is perpendicular with line TP, so the gradient tangent line h : </li></ul>
6. 6. <ul><li>Equation of tangent line h is : </li></ul>
7. 7. <ul><li>because T(x1,y1) on </li></ul><ul><li>L </li></ul><ul><li>So it occures : </li></ul>
8. 8. <ul><li>then sub stitute equation (1) and (2) </li></ul><ul><li>Based on above description , the tangent line equation on circle L </li></ul><ul><li>pass through the tangent point T(x 1 ,y 1 ) </li></ul><ul><li>found with : </li></ul>
9. 9. Example <ul><li>Determine the equestion of the tangent line to the circle: </li></ul><ul><li>X 2 +y 2 =5 at point (-2,1) </li></ul><ul><li>(x+2) 2 +(y+3) 2 =40 at point of(4,-1) </li></ul>
10. 10. <ul><li>a. X 2 +y 2 =5 at point (-2,1) </li></ul>
11. 11. <ul><li>b. (x+2) 2 +(y+3) 2 =40 at point of(4,-1) </li></ul>