Maths-
General
Easy

Question

Assertion (A): The lines represented by 3 x squared plus 10 x y plus 3 y squared minus 16 x minus 16 y plus 16 equals 0 and x+ y=2 do not form a triangle
Reason (R): The above three lines concur at (1,1)

  1. Both A and R are true and R is the correct explanation A
  2. Both A and R are true but R is not the correct explanation of A
  3. A is true but R is false
  4. A is false but R is true

hintHint:

Find the point of intersection of the given straight lines. If they do not have common point of intersection then, we can say that the given straight lines form a triangle.

The correct answer is: Both A and R are true and R is the correct explanation A


    Given That:
    Assertion (A): The lines represented by 3 x squared plus 10 x y plus 3 y squared minus 16 x minus 16 y plus 16 equals 0 and x+ y=2                                                     do not form a triangle
    Reason (R): The above three lines concur at (1,1)
    >>> Let us say that the given statements are true, Then:
    >>> The given lines should pass through the point of concurrency(1,1).
    >>> Therefore:
    3 x squared plus 10 x y plus 3 y squared minus 16 x minus 16 y plus 16 equals 0
    3+10+3-16-16+16=0
    0=0
    >>> Similarly, x + y = 2
    1 + 1 = 2
    2 = 2.
    >>> Therefore, all the three lines satisfies the given point.
    >>> Hence, we can clearly say that the given straight lines never form a triangle since they all have a common intersection point.

    Both Assertion and Reason are correct and the Reason is the correct explanation of Assertion.

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