If the lines p(p2 + 1)x - y + q = 0 and (p2 + 1)2x + (p2 + 1)y + 2

1.	If the lines p(p2 + 1)x - y + q = 0 and (p2 + 1)2x + (p2 + 1)y + 2q = 0 are perpendicula to the same line, then find the vaue of p will be,1. 12. -13. 04. -2
Answer» Correct Answer - Option 2 : -1 Concept: The general equation of a line is y = mx + c -----(A) Where m is the slope and c is any constant. The slope of parallel lines is equal. Slope of the perpendicular line have their product = -1 Calculation: The given lines are, p(p2 + 1)x - y + q = 0 ------(i) and (p2 + 1)2x + (p2 + 1)y + 2q = 0 -------(ii) Slope of the lines (i) is, \(\frac{-p(p^2+1)}{-1}\) i.e, p(p² + 1) Similarly slope of the line (ii) is, \(-\frac{(p^2+1)^2}{p^2+1}\) i.e, -(p² +1) Since the given lines are perpendicular to the same line, therefore, these lines are parallel which gives the lines have equal slope. ⇒ p(p2 + 1) = -(p2 +1) ⇒ (p² + 1) (p + 1) = 0 but p² + 1 ≠ 0 ⇒ p + 1 = 0 ⇒ p = -1

If the lines p(p2 + 1)x - y + q = 0 and (p2 + 1)2x + (p2 + 1)y + 2q = 0 are perpendicula to the same line, then find the vaue of p will be,1. 12. -13. 04. -2

Answer» Correct Answer - Option 2 : -1

Concept:

The general equation of a line is y = mx + c -----(A)

Where m is the slope and c is any constant.

The slope of parallel lines is equal.
Slope of the perpendicular line have their product = -1

Calculation:

The given lines are, p(p2 + 1)x - y + q = 0 ------(i)

and (p2 + 1)2x + (p2 + 1)y + 2q = 0 -------(ii)

Slope of the lines (i) is, \(\frac{-p(p^2+1)}{-1}\) i.e, p(p² + 1)

Similarly slope of the line (ii) is, \(-\frac{(p^2+1)^2}{p^2+1}\) i.e, -(p² +1)

Since the given lines are perpendicular to the same line, therefore, these lines are parallel which gives the lines have equal slope.

⇒ p(p2 + 1) = -(p2 +1)

⇒ (p² + 1) (p + 1) = 0

but p² + 1 ≠ 0

⇒ p + 1 = 0

⇒ p = -1

Discussion

No Comment Found

Related InterviewSolutions

The sequence \((\frac{3^n}{n!} )\) is1. bounded2. unbounded3. convergent4. monotonic
The sequence \(((1+\frac{1}{n})^\frac{1}{n})\) is1. bounded2. unbounded3. only lower bounded4. only upper bounded
Three forces P, Q, R are acting at a point in a plane. The angle between P and Q, Q and R are 150° and 120° respectively, then for equilibrium, forces P, Q, R are in the ratio1. 1 ∶ 2 ∶ 32. 1 ∶ 2 ∶ √3 3. 3 ∶ 2 ∶ 14. √3 ∶ 2 ∶ 1
The necessary condition for a series \(\sum {{u_n}} \) to converge is that1. \(\mathop {\lim }\limits_{n \to \infty } {u_n} \to 0\)2. \(\mathop {\lim }\limits_{n \to \infty } {u_n} =1\)3. \(\mathop {\lim }\limits_{n \to \infty } {u_n} = -1\)4. None of these
The set of all limit point of a set S is called 1. subset2. derived set3. closed set4. open set
Consider the function\({\rm{\;f\;}}\left( {\rm{x}} \right) = {{\rm{x}}^2} - {\rm{x}} - 2\). The maximum value of f (x) in the closed interval [- 4, 4] is1. 182. 103. 24. 4
A function f defined on a closed interval [a, b] is said to be continuous at the end point if1. it is continuous at the right at 'a'2. it is discontinuous at the right at 'a'3. the value of 'a' is zero4. f(a) = f(b)
Every bounded sequence has a convergent subsequence. This is a statement of 1. Bolzano-Weierstrass Theorem2. Cauchy Theorem3. Taylor's Theorem4. None of these
A sequence (sn) of real numbers is called a Cauchy sequence if1. |sn + sk| ε
A sequence Sn is bounded is there exists a number K > 0 such that1. |Sn| > K2. |Sn| = K3. |Sn| < K4. None of these