Question -
Answer -
The equation of the given curve is┬аy┬а=┬аx3┬атИТ11x┬а+ 5.
The equation of the tangent to the givencurve is given as┬аy┬а=┬аx┬атИТ 11 (which is of theform┬аy┬а=┬аmx┬а+┬аc).
тИ┤Slope of the tangent = 1
Now, the slope of the tangent to the given curve atthe point (x,┬аy) is given by,┬а
Then, we have:
When┬аx┬а= 2,┬аy┬а=(2)3┬атИТ 11 (2) + 5 = 8 тИТ 22 + 5 = тИТ9.
When┬аx┬а= тИТ2,┬аy┬а=(тИТ2)3┬атИТ 11 (тИТ2) + 5 = тИТ8 + 22 + 5 = 19.
Hence, the required points are (2, тИТ9) and (тИТ2, 19). But,both these points should satisfy the equation of the tangent as there would bepoint of contact┬аbetween tangent and the curve. тИ┤┬а(2, тИТ9) is the required point as (тИТ2, 19) is notsatisfying the given equation of tangent.