Let A (a, 0) and B(b, 0) are the points on the curve y = x 2 –6x +5 in the cartesian coordinate system amd C is a point on arc AB , then the maximum value of | CA×CB| is

Question

Let A (a, 0) and B(b, 0) are the points on the curve y = x 2 –6x +5 in the cartesian coordinate system amd C is a point on arc AB , then the maximum value of | CA×CB| is

Aditya Gupta · Answer

obviously a and b are roots of eqn y = x 2 –6x +5 since y is 0 at these pts. since y = x 2 –6x +5= (x – 5)(x – 1) hence A(1, 0) and B(5, 0) clearly | CA×CB |= |CA.CB.sin(t)| where t is angle ACB. = 2*| ½ CA.CB.sin(t)| but ½ CA.CB.sin(t) = A= area of triangle ABC (std formula) so, | CA×CB |= 2*A. to maximise | CA×CB |, we need to maximise A. since only pt C is variable, while AB is constant (=4), so we can write A= ½ AB*h, where h is the height of perpendicular from C on base AB. since AB is constant, we need to maximise h in order to maximise A. You ll note after drawing the graph of curve y = x 2 –6x +5 that its min value occurs when y’ = 0 or at x=3. since h= magnitude of y coordinate of C, h is max when C’s magnitude of y coordinate is max, which clearly happens at x=3. when x=3, y= – 4. hence h|max= |-4|= 4 whence A|max= ½ *AB*h= ½ *4*4= 8 so, CA×CB |max= 2*A|max = 2*8 = 16 KINDLY APPROVE :))

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Let A (a, 0) and B(b, 0) are the points on the curve y = x 2 –6x +5 in the cartesian coordinate system amd C is a point on arc AB , then the maximum value of | CA×CB| is

Let A (a, 0) and B(b, 0) are the points on the curve y = x²–6x +5 in the cartesian coordinate system amd C is a point on arc AB , then the maximum value of | CA×CB| is

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Let A (a, 0) and B(b, 0) are the points on the curve y = x 2 –6x +5 in the cartesian coordinate system amd C is a point on arc AB , then the maximum value of | CA×CB| is

Let A (a, 0) and B(b, 0) are the points on the curve y = x2–6x +5 in the cartesian coordinate system amd C is a point on arc AB , then the maximum value of | CA×CB| is

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Let A (a, 0) and B(b, 0) are the points on the curve y = x²–6x +5 in the cartesian coordinate system amd C is a point on arc AB , then the maximum value of | CA×CB| is