For all values of theta,the line (2 cos theta | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) The given equation is $(2 \cos 	heta + 3 \sin 	heta) x + (3 \cos 	heta - 5 \sin 	heta) y - (5 \cos 	heta - 2 \sin 	heta) = 0$. Rearranging t

Vedclass · Accepted Answer

$(1, 1)$

Vedclass · Answer

(B) The given equation is $(2 \cos 	heta + 3 \sin 	heta) x + (3 \cos 	heta - 5 \sin 	heta) y - (5 \cos 	heta - 2 \sin 	heta) = 0$. Rearranging the terms by grouping $\cos 	heta$ and $\sin 	heta$: $\cos 	heta (2x + 3y - 5) + \sin 	heta (3x - 5y + 2) = 0$. For this equation to hold for all values of $	heta$,the coefficients of $\cos 	heta$ and $\sin 	heta$ must be zero independently: $2x + 3y - 5 = 0$ (Equation $1$) $3x - 5y + 2 = 0$ (Equation $2$) Multiplying Equation $1$ by $5$ and Equation $2$ by $3$: $10x + 15y - 25 = 0$ $9x - 15y + 6 = 0$ Adding these two equations: $19x - 19 = 0 \implies x = 1$. Substituting $x = 1$ into Equation $1$: $2(1) + 3y - 5 = 0 \implies 3y = 3 \implies y = 1$. Thus,the fixed point is $(1, 1)$.

For all values of $\theta$,the line $(2 \cos \theta + 3 \sin \theta) x + (3 \cos \theta - 5 \sin \theta) y - (5 \cos \theta - 2 \sin \theta) = 0$ passes through which fixed point?

Similar Questions

If the three distinct lines $x + 2ay + a = 0$,$x + 3by + b = 0$,and $x + 4ay + a = 0$ are concurrent,then the point $(a, b)$ lies on a

The line parallel to the $x$-axis and passing through the intersection of the lines $ax + 2by + 3b = 0$ and $bx - 2ay - 3a = 0$,where $(a, b) \ne (0, 0)$ is

The equation of the straight line passing through the intersection of the lines $x - 2y = 1$ and $x + 3y = 2$ and parallel to $3x + 4y = 0$ is

The lines $x-2y+1=0$,$2x-3y-1=0$,and $3x-y+k=0$ are concurrent. The angle between the lines $3x-y+k=0$ and $mx-3y+6=0$ is $45^{\circ}$. If $m$ is an integer,then $m-k=$

Consider the set of all lines $px + qy + r = 0$ such that $3p + 2q + 4r = 0$. Which one of the following statements is true?

Vedclass Test Series

Exam Paper Generator

Online Exam Module