Question

Let f(x) = x². There are two lines with positive slope that are tangent to the parabola and that pass through the point (5, 22.75). Find the equation of the line with the smaller slope.

Answer 1

Soludion: Given: f(x) = x² is an equation of Pasobola. There are two fangent lines passing through point. (5, 22.75), you have to find equation of fangent line with smaller slope. Step 1 write equation of line bassing through (5,22. 75) with variable slope. Let sloße=m Apply point- slope form (4-22.75 ) = m ( x-5) Y = m(x-5) + 22. 75. – 0 Step: IT Apply condition of tangent of above line on Parabola S00) = x² - ( Abouce line intersect Parabola fre) = xc² at only one point for fixed value of 'm. x² = m(or-5) + 22. 75 x² = mx-5m + 2 2. 75. x² - mac + (5m-22. 75) = 0 quada fic in bed

it descriminant (D) = b²-4ac, should be zero. (-m - 4.1.15m-22.75)=0 aac²+bx+C =0 D= 6²-4.6.0 m² - com +91=0 (Factorize) m-13m 7m +91=0 mcm-15) - 7 (m-13)=0 (m-a (m-13) = 0 m. 7=0 of m=15 m= 7 of m= 15. Cret two possible value of m. i. e get two angent line with slope (M) = II, 15. Smaller slope 7 write equation of fangent line in point-slope form. Slokecm) - 7 Point (aco, y) = (5,22.25) Equation: (4-9 ) = m(x-x1) (9.22.45) = 7(x-5) y- 22.75= 73 - 35. y 7x - 35 + 92.75 - Y= 78 - 12.25. I ANS