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TS EAMCET · Maths · Parabola

Find the equation to the parabola, whose axis parallel to the \(y\)-axis and which passes through the points \((0,4),(1,9)\) and \((4,5)\) is

  1. A \(y=-x^2+x+4\)
  2. B \(y=-x^2+x+1\)
  3. C \(y=\frac{-19}{12} x^2+\frac{79}{12} x+4\)
  4. D \(y=\frac{-19}{12} x^2+\frac{89}{12}+1\)
Verified Solution

Answer & Solution

Correct Answer

(C) \(y=\frac{-19}{12} x^2+\frac{79}{12} x+4\)

Step-by-step Solution

Detailed explanation

The equation of parabola parallel to \(y\)-axis is \(y=A x^2+B x+C\) ...(i) The point \((0,4),(1,9)\) and \((4,5)\) lies on Eq. (i). Then, \(\quad 4=0+0+C \Rightarrow C=4\) ...(ii) \(9=A+B+C\) or \(\quad 9=A+B+4 \quad(\because C=4)\) \(A+B=5\) ...(iii) and…