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100 points for $49 worth of Veritas practice GMATs FREE VERITAS PRACTICE GMAT EXAMS Earn 10 Points Per Post Earn 10 Points Per Thanks Earn 10 Points Per Upvote ## Coordinate plane tagged by: BTGmoderatorRO ##### This topic has 1 expert reply and 0 member replies ## Coordinate plane The equation x = $$^{2y^2}$$ + 5y - 17, describes a parabola in the xy coordinate plane. If line l, with slope of 3, intersects the parabola in the upper-left quadrant at x = -5, the equation for l is A. 3x + y + 15 = 0 B. y - 3x - 11 = 0 C. -3x + y - 16.5 = 0 D. -2x - y - 7 = 0 E. -3x + y + 13.5 = 0 ### GMAT/MBA Expert GMAT Instructor Joined 04 Oct 2017 Posted: 551 messages Followed by: 11 members Upvotes: 180 Top Reply Hello Roland2rule. Let's take a look. The equation of the parabola is $$x=2y^2+5y-17.$$ The equation of the line L is $$L:\ y-y_0=m\left(x-x_0\right)\Leftrightarrow\ \ y-y_0=3\left(x-x_0\right).$$ We just have to find a point that is on the line. In order to find it we have to solve the quadratic equation $$-5=2y^2+5y-17\ \Leftrightarrow\ \ 2y^2+5y-12=0.$$ The Roots of this equation are given by $$y_{1,2}=\frac{-5\pm\sqrt{5^2-4\cdot2\cdot\left(-12\right)}}{2\cdot2}\ =\ \frac{-5\pm\sqrt{25+96}}{4}=\frac{-5\pm\sqrt{121}}{4}=\ \frac{-5\pm11}{4}.$$ The two solutions are y=6/4=3/2 and y=-16/4=-4. Since the line intersects the parabola in the upper-left quadrant at x = -5, then we have to select the positive solution. Therefore, the point of intersection is (-5,3/2). So, the equation of the line is $$L\ :\ y-\frac{3}{2}=3\left(x-\left(-5\right)\right)\ \Leftrightarrow\ \frac{2y-3}{2}=3x+15\ \Leftrightarrow\ 2y-3=6x+30$$ $$\ \Leftrightarrow\ \ -6x+2y-33=0\ \Leftrightarrow\ -3x+y-16.5=0.$$ Hence, the correct option is C. I hope this explanation may help you. Feel free to ask me again if you have a doubt. Regards. _________________ GMAT Prep From The Economist We offer 70+ point score improvement money back guarantee. Our average student improves 98 points. Free 7-Day Test Prep with Economist GMAT Tutor - Receive free access to the top-rated GMAT prep course including a 1-on-1 strategy session, 2 full-length tests, and 5 ask-a-tutor messages. Get started now. • Free Trial & Practice Exam BEAT THE GMAT EXCLUSIVE Available with Beat the GMAT members only code • Free Practice Test & Review How would you score if you took the GMAT Available with Beat the GMAT members only code • Award-winning private GMAT tutoring Register now and save up to$200

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