| Assertion [A]: Tangent to the curve \[y={{x}^{2}}-7x+12\] at the points (3, 0) and (4, 0) are at right angles. |
| Reason [R]: For perpendicular lines, product of slopes of lines is -1. |
A) Both A and R are individually true and R is the correct explanation of A.
B) Both A and R are individually true and R is not the correct explanation of A.
C) 'A' is true but 'R' is false
D) 'A' is false but 'R' is true
E) Both A and R are false.
Correct Answer: A
Solution :
Given \[y={{x}^{2}}-7x+12\] \[\Rightarrow \,\,\,\,\,\,\,\,\,\,\,\,\,\,\frac{dy}{dx}=2x-7\] Slope of tangent at point \[\left( 3,0 \right),\text{ }{{m}_{1}}=2\times 3-7=-1\] Slope of tangent at point \[\left( 4,0 \right),\text{ }{{m}_{2}}\,=\,2\times 4-7=1\] Here \[~{{m}_{1}}{{m}_{2}}=-1\times 1=-1\] \[\Rightarrow \] tangent are perpendicular to each other \[\therefore \] Assertion [A] is true. Also Reason (R) is product of slope of lines is -1 \[\therefore \] Reason (R) is true and is correct explanation of Assertion [A]. Hence option [A] is the correct answer.
You need to login to perform this action.
You will be redirected in
3 sec
